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  <link:labelLink xlink:role="http://www.xbrl.org/2003/role/link" xlink:type="extended">
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Accumulated Amortization</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAccumulatedAmortization" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_019ce734-5ba0-75e6-afd6-9f0708b76644_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt and Equity Securities, FV-NI [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:to="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock_019ce734-5c52-7f42-bfb2-b0d992b3f512_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Prior Year Loss Development for the AmTrust Reinsurance Legacy Operations</link:label>
    <link:label id="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock_label_en-US" xlink:label="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of prior year loss development by line of business [Table Text Block]</link:label>
    <link:label id="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock_documentation_en-US" xlink:label="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of prior year loss development by line of business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:href="kg-20260331.xsd#kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:to="lab_kg_ScheduleOfPriorYearLossDevelopmentByLineOfBusinessTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined</link:label>
    <link:label id="lab_ecd_AwardTmgPredtrmndFlag_label_en-US" xlink:label="lab_ecd_AwardTmgPredtrmndFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Predetermined [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgPredtrmndFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgPredtrmndFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgPredtrmndFlag" xlink:to="lab_ecd_AwardTmgPredtrmndFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFileNumber_019ce734-5c52-7635-80a4-a9333a349b9a_terseLabel_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:label id="lab_dei_EntityFileNumber_label_en-US" xlink:label="lab_dei_EntityFileNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity File Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFileNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFileNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFileNumber" xlink:to="lab_dei_EntityFileNumber" xlink:type="arc" order="1"/>
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    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Floor</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Floor</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:to="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_019ce734-5c52-72d3-a242-1e743224e420_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid-in Capital [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapitalMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapitalMember" xlink:to="lab_us-gaap_AdditionalPaidInCapitalMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_019ce734-5c52-7897-a626-5e2ff5c5288f_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quarterly brokerage fee, above portfolio threshold, percent of average holdings</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Quarterly Brokerage Fee, Above Portfolio Threshold, Percent of Average Holdings</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Quarterly Brokerage Fee, Above Portfolio Threshold, Percent of Average Holdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:to="lab_kg_RelatedPartyTransactionQuarterlyBrokerageFeeAbovePortfolioThresholdPercentOfAverageHoldings" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TabularListTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Tabular List, Table</link:label>
    <link:label id="lab_ecd_TabularListTableTextBlock_label_en-US" xlink:label="lab_ecd_TabularListTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Tabular List [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TabularListTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TabularListTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TabularListTableTextBlock" xlink:to="lab_ecd_TabularListTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_019ce734-5cd9-7863-9dcd-2a4516218313_terseLabel_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Recently Adopted Accounting Standards and Recently Issued Accounting Standards Not Yet Adopted</link:label>
    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:to="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_019ce734-5c52-7dd3-b141-5b6434169848_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Quota Share Arrangements with AmTrust</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DiversifiedLegacySegmentMember_019ce734-5ba0-72b4-b50c-e46dc77cdf84_verboseLabel_en-US" xlink:label="lab_kg_DiversifiedLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diversified Legacy Reinsurance</link:label>
    <link:label id="lab_kg_DiversifiedLegacySegmentMember_label_en-US" xlink:label="lab_kg_DiversifiedLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diversified Legacy Segment [Member]</link:label>
    <link:label id="lab_kg_DiversifiedLegacySegmentMember_documentation_en-US" xlink:label="lab_kg_DiversifiedLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diversified Legacy Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedLegacySegmentMember" xlink:href="kg-20260331.xsd#kg_DiversifiedLegacySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DiversifiedLegacySegmentMember" xlink:to="lab_kg_DiversifiedLegacySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_019ce734-5cd9-7399-b67d-f482fd0b583d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Carrying Value and Fair Value of Senior Notes</link:label>
    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, by Balance Sheet Grouping [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByBalanceSheetGroupingTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:to="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet_019ce734-5cd9-73be-979c-a9a12e822bc7_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in unearned premiums</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">(Increase) Decrease in Unearned Premiums, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInUnearnedPremiumsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInUnearnedPremiumsNet"/>
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    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_019ce734-5c52-7384-99c4-1bd317f36b25_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByMeasurementBasisAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Basis [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByMeasurementBasisAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByMeasurementBasisAxis" xlink:to="lab_us-gaap_FairValueByMeasurementBasisAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAxis_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation:</link:label>
    <link:label id="lab_ecd_AdjToCompAxis_label_en-US" xlink:label="lab_ecd_AdjToCompAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAxis"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_019ce734-5c52-78a6-b2a7-bd105faf9acd_verboseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:to="lab_us-gaap_RelatedPartyTransactionsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote</link:label>
    <link:label id="lab_ecd_NamedExecutiveOfficersFnTextBlock_label_en-US" xlink:label="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Named Executive Officers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NamedExecutiveOfficersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NamedExecutiveOfficersFnTextBlock" xlink:to="lab_ecd_NamedExecutiveOfficersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_019ce734-5c52-76d9-baab-5ebb5a747969_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of premiums written, net of cost of unaffiliated inuring reinsurance from related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Premium Written, Net of Cost of Unaffiliated Inuring Reinsurance From Related Party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Premium Written, Net of Cost of Unaffiliated Inuring Reinsurance From Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_019ce734-5c52-7ca9-a957-819367fe1d23_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_label_en-US" xlink:label="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Amortized Cost Basis</link:label>
    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Amortized Cost Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesAmortizedCostBasis" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesAmortizedCostBasis" xlink:to="lab_kg_FixedMaturitiesAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_019ce734-5c52-7c93-b856-7cee6beff488_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Stock by Class [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfStockByClassTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock, Class of Stock [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfStockByClassTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfStockByClassTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfStockByClassTable" xlink:to="lab_us-gaap_ScheduleOfStockByClassTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_019ce734-5ba0-7ffa-ab82-54c5209d8a97_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of ceded underwriting risk in exchange for ceding fee</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Ceded Underwriting Risk in Exchange for Ceding Fee</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Ceded Underwriting Risk in Exchange for Ceding Fee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:to="lab_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustQuotaShareMember_019ce734-5cd9-7613-8dcc-d0cff1a177f9_terseLabel_en-US" xlink:label="lab_kg_AmTrustQuotaShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share</link:label>
    <link:label id="lab_kg_AmTrustQuotaShareMember_label_en-US" xlink:label="lab_kg_AmTrustQuotaShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share [Member]</link:label>
    <link:label id="lab_kg_AmTrustQuotaShareMember_documentation_en-US" xlink:label="lab_kg_AmTrustQuotaShareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustQuotaShareMember" xlink:href="kg-20260331.xsd#kg_AmTrustQuotaShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustQuotaShareMember" xlink:to="lab_kg_AmTrustQuotaShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_019ce734-5ba1-7ef3-8f9c-e40abcc4f79c_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, loan agreement, obligation threshold</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Loan Agreement, Obligation Threshold</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Loan Agreement, Obligation Threshold</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionLoanAgreementObligationThreshold"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:to="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_019ce734-5c52-72d2-99c9-17fcf7154667_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_019ce734-5c52-7cd3-9735-0cb71d90cf3c_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Assets held for sale</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation, Amount</link:label>
    <link:label id="lab_ecd_AdjToCompAmt_label_en-US" xlink:label="lab_ecd_AdjToCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToCompAmt" xlink:to="lab_ecd_AdjToCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_019dcdb8-9e2d-75b5-8b8f-3c004d5d4bd2_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration risk, percentage</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskPercentage1_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskPercentage1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskPercentage1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskPercentage1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskPercentage1" xlink:to="lab_us-gaap_ConcentrationRiskPercentage1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputCapRateMember_019d33da-9605-787c-a3bd-e094e4a53345_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputCapRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exit Cap Rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputCapRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputCapRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Cap Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputCapRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputCapRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputCapRateMember" xlink:to="lab_us-gaap_MeasurementInputCapRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_019ce734-5ba0-78c7-868a-4dc867463d40_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: unamortized fair value adjustment</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Unamortized Discount (Premium) and Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:to="lab_us-gaap_DebtInstrumentUnamortizedDiscountPremiumAndDebtIssuanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_019ce734-5c52-7bff-b3d0-8015885e762b_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Other Operating Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOtherOperatingAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:to="lab_us-gaap_IncreaseDecreaseInOtherOperatingAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensation_019dde9f-5430-7369-be4d-c3786804f604_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensation_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Noncash Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensation" xlink:to="lab_us-gaap_ShareBasedCompensation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_019e0391-be14-7dc4-a7df-76afec233ca5_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Options</link:label>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_label_en-US" xlink:label="lab_us-gaap_EmployeeStockOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Option [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeStockOptionMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeStockOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EmployeeStockOptionMember" xlink:to="lab_us-gaap_EmployeeStockOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock_019ce734-5ba1-7a39-9ee0-85850f5108e6_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Amortized Cost, Gross Unrealized Gains and Losses and Fair Value on Fixed Maturities</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock_label_en-US" xlink:label="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments Reconciliation [Table Text Block]</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock_documentation_en-US" xlink:label="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Investments Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:href="kg-20260331.xsd#kg_ScheduleOfInvestmentsReconciliationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:to="lab_kg_ScheduleOfInvestmentsReconciliationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquity_019ce734-5ba0-7982-9dde-96754ef8db9a_totalLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total shareholders&#8217; equity</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019ce734-5ba0-707b-9c0f-b95468bd2da5_periodStartLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Beginning balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_019ce734-5ba0-7c4a-b6dc-0d5d1ddec498_periodEndLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Ending balance</link:label>
    <link:label id="lab_us-gaap_StockholdersEquity_label_en-US" xlink:label="lab_us-gaap_StockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquity"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquity" xlink:to="lab_us-gaap_StockholdersEquity" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome_019ce734-5ba0-7503-a4e4-b18ee6f826ea_terseLabel_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome_label_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accrued Investment Income</link:label>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome_documentation_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Accrued Investment Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome" xlink:href="kg-20260331.xsd#kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome" xlink:to="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_019ce734-5ba0-7097-b9e8-7ad8db178750_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Available-for-sale Securities [Table]</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleTable_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingPoliciesProcLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingPoliciesProcLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingPoliciesProcLineItems" xlink:to="lab_ecd_InsiderTradingPoliciesProcLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_019ce734-5c52-72ec-a9e3-7d3fd4185c0f_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Authorized share capital (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesAuthorized"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesAuthorized" xlink:to="lab_us-gaap_CommonStockSharesAuthorized" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipHeldDirectlyMember_019df411-0d57-738b-bb90-febb757aaca0_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Held Directly</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldDirectlyMember_label_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Directly [Member]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldDirectlyMember_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Directly</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipHeldDirectlyMember" xlink:href="kg-20260331.xsd#kg_CommonStockOwnershipHeldDirectlyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockOwnershipHeldDirectlyMember" xlink:to="lab_kg_CommonStockOwnershipHeldDirectlyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainContingenciesTable_019ce734-5cd9-7d61-b7c8-be6c2bddd2a1_terseLabel_en-US" xlink:label="lab_us-gaap_GainContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Table]</link:label>
    <link:label id="lab_us-gaap_GainContingenciesTable_label_en-US" xlink:label="lab_us-gaap_GainContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainContingenciesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainContingenciesTable" xlink:to="lab_us-gaap_GainContingenciesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_019ce734-5c52-777b-9b87-9f0e786158e2_terseLabel_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable: (Allowance for expected credit losses: 2026: $2; 2025: $2)</link:label>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_019ce734-5c52-734a-9b7e-3bf7bb552709_verboseLabel_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable</link:label>
    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_label_en-US" xlink:label="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funds Held under Reinsurance Agreements, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FundsHeldUnderReinsuranceAgreementsAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:to="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_019ce734-5c52-73b7-bd6a-03e3f24dfd89_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net (includes $0 and $2 from related parties in 2026 and 2025, respectively. Allowance for expected credit losses: 2026 - $14; 2025 - $14)</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_019ce734-5c52-7ee4-a89d-b60998531e3b_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsReceivableAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsReceivableAtCarryingValue" xlink:to="lab_us-gaap_PremiumsReceivableAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CoverAbstract_019ce734-5c52-74c3-96a6-e820728f0b2c_terseLabel_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:label id="lab_dei_CoverAbstract_label_en-US" xlink:label="lab_dei_CoverAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cover [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CoverAbstract" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CoverAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CoverAbstract" xlink:to="lab_dei_CoverAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_019ce734-5cd9-7323-817f-7647c41641b8_terseLabel_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement</link:label>
    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Portion at Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PortionAtFairValueFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_019ce734-5c52-78e4-85e5-3b7577dcd3ba_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets Held for Sale</link:label>
    <link:label id="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations, Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:to="lab_us-gaap_DisposalGroupsIncludingDiscontinuedOperationsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_MaximumMember_019ce734-5ba1-7f48-bb04-ae185bfe2b10_terseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum</link:label>
    <link:label id="lab_srt_MaximumMember_019d33da-9605-777a-9622-fcf7c54f3718_verboseLabel_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">High</link:label>
    <link:label id="lab_srt_MaximumMember_label_en-US" xlink:label="lab_srt_MaximumMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maximum [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_MaximumMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_MaximumMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_MaximumMember" xlink:to="lab_srt_MaximumMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_019ce734-5c52-728f-929e-44271903d432_negatedTerseLabel_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Discount for present value</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_label_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Fair Value Discount</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_documentation_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Fair Value Discount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:href="kg-20260331.xsd#kg_LesseeOperatingLeaseLiabilityFairValueDiscount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:to="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_019ce734-5cd9-778c-b09a-afcc37e6c837_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedStockMember_019d33f9-faa8-7e87-b69b-0900f7591385_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Stock</link:label>
    <link:label id="lab_us-gaap_RestrictedStockMember_label_en-US" xlink:label="lab_us-gaap_RestrictedStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedStockMember" xlink:to="lab_us-gaap_RestrictedStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember_019d33da-9605-7229-97c7-9e28c7989638_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Value Change - Company Performance</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember_label_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company Multiples [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company Multiples</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:href="kg-20260331.xsd#kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:to="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyMultiplesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgTotalCompAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgTotalCompAmt" xlink:to="lab_ecd_NonPeoNeoAvgTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_019ce734-5ba0-7d8e-88c8-75a3079ad1ee_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentLineItems_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentLineItems" xlink:to="lab_us-gaap_DebtInstrumentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_TerryLeeLedbetterMember_019dcda5-fafc-753f-98f2-f3d93daadc68_terseLabel_en-US" xlink:label="lab_kg_TerryLeeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Terry Lee Ledbetter</link:label>
    <link:label id="lab_kg_TerryLeeLedbetterMember_label_en-US" xlink:label="lab_kg_TerryLeeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Terry Lee Ledbetter [Member]</link:label>
    <link:label id="lab_kg_TerryLeeLedbetterMember_documentation_en-US" xlink:label="lab_kg_TerryLeeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Terry Lee Ledbetter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TerryLeeLedbetterMember" xlink:href="kg-20260331.xsd#kg_TerryLeeLedbetterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_TerryLeeLedbetterMember" xlink:to="lab_kg_TerryLeeLedbetterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCancellationNoticePeriod_019ce734-5cd9-7fc8-8d31-4595316f3e24_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cancellation notice period</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCancellationNoticePeriod_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Cancellation Notice Period</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCancellationNoticePeriod_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Cancellation Notice Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionCancellationNoticePeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:to="lab_kg_RelatedPartyTransactionCancellationNoticePeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote</link:label>
    <link:label id="lab_ecd_AdjToNonPeoNeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Non-PEO NEO Compensation Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToNonPeoNeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:to="lab_ecd_AdjToNonPeoNeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_019ce734-5c52-7ccd-9986-b584282ef714_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DirectPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectPremiumsEarned" xlink:to="lab_us-gaap_DirectPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ExternalCreditRatingStandardPoorsMember_019ce734-5cd9-7bca-a019-2a7099decafd_terseLabel_en-US" xlink:label="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">External Credit Rating, Standard &amp; Poor's [Domain]</link:label>
    <link:label id="lab_srt_ExternalCreditRatingStandardPoorsMember_label_en-US" xlink:label="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">External Credit Rating, Standard &amp; Poor's [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ExternalCreditRatingStandardPoorsMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ExternalCreditRatingStandardPoorsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ExternalCreditRatingStandardPoorsMember" xlink:to="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Disqualification of Tax Benefits, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToDisqualificationOfTaxBenefitsAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_019ce734-5c52-7b04-80e8-7e0f3d8a328f_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gain on bargain purchase</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_019ce734-5c52-7ec6-8dbf-08e41ed64323_negatedLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Bargain purchase gain</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Bargain Purchase, Gain Recognized, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:to="lab_us-gaap_BusinessCombinationBargainPurchaseGainRecognizedAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrTrmntdFlag" xlink:to="lab_ecd_NonRule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SegmentConcentrationRiskMember_019dcdb8-9e2d-7d01-b104-60105a858f4b_terseLabel_en-US" xlink:label="lab_kg_SegmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Concentration Risk</link:label>
    <link:label id="lab_kg_SegmentConcentrationRiskMember_label_en-US" xlink:label="lab_kg_SegmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Concentration Risk [Member]</link:label>
    <link:label id="lab_kg_SegmentConcentrationRiskMember_documentation_en-US" xlink:label="lab_kg_SegmentConcentrationRiskMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Segment Concentration Risk [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SegmentConcentrationRiskMember" xlink:href="kg-20260331.xsd#kg_SegmentConcentrationRiskMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SegmentConcentrationRiskMember" xlink:to="lab_kg_SegmentConcentrationRiskMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityShellCompany_019ce734-5c52-752f-8076-f590a02934f0_terseLabel_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:label id="lab_dei_EntityShellCompany_label_en-US" xlink:label="lab_dei_EntityShellCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Shell Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityShellCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityShellCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityShellCompany" xlink:to="lab_dei_EntityShellCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentTable_019ce734-5ba0-79ec-b52f-d90efbfdf889_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Long-term Debt Instruments [Table]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentTable_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentTable" xlink:to="lab_us-gaap_DebtInstrumentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupMember_019ce734-5c52-7409-b0a4-961d6990c540_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group</link:label>
    <link:label id="lab_kg_KestrelGroupMember_label_en-US" xlink:label="lab_kg_KestrelGroupMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Group [Member]</link:label>
    <link:label id="lab_kg_KestrelGroupMember_documentation_en-US" xlink:label="lab_kg_KestrelGroupMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Group</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupMember" xlink:href="kg-20260331.xsd#kg_KestrelGroupMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupMember" xlink:to="lab_kg_KestrelGroupMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SummaryOfOtherInvestmentsTableTextBlock_019ce734-5c52-7cdf-bde3-37185bd75e85_terseLabel_en-US" xlink:label="lab_kg_SummaryOfOtherInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Composition of Other Investments</link:label>
    <link:label id="lab_kg_SummaryOfOtherInvestmentsTableTextBlock_label_en-US" xlink:label="lab_kg_SummaryOfOtherInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Summary of Other Investments [Table Text Block]</link:label>
    <link:label id="lab_kg_SummaryOfOtherInvestmentsTableTextBlock_documentation_en-US" xlink:label="lab_kg_SummaryOfOtherInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Summary of Other Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SummaryOfOtherInvestmentsTableTextBlock" xlink:href="kg-20260331.xsd#kg_SummaryOfOtherInvestmentsTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SummaryOfOtherInvestmentsTableTextBlock" xlink:to="lab_kg_SummaryOfOtherInvestmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve_019ce734-5c52-7e73-9ea0-68f1f6f9357f_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Liability for Claims and Claims Adjustment Expense Reserve</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:to="lab_us-gaap_IncreaseDecreaseInLiabilityForClaimsAndClaimsAdjustmentExpenseReserve" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_019ce734-5cd9-7edd-a606-6efd4f7e5763_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfStockholdersEquityAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Stockholders' Equity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfStockholdersEquityAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfStockholdersEquityAbstract" xlink:to="lab_us-gaap_StatementOfStockholdersEquityAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_019ce734-5cd9-7bd5-a505-3220e7f79a2e_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Segments</link:label>
    <link:label id="lab_us-gaap_OperatingSegmentsMember_label_en-US" xlink:label="lab_us-gaap_OperatingSegmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Segments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingSegmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingSegmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingSegmentsMember" xlink:to="lab_us-gaap_OperatingSegmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgMnpiCnsdrdFlag_label_en-US" xlink:label="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Considered [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMnpiCnsdrdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMnpiCnsdrdFlag" xlink:to="lab_ecd_AwardTmgMnpiCnsdrdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_019ce734-5c52-782a-875a-7c33c940c6a5_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss from continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperations_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperations" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationStockConversionRatio_019ce734-5c52-7150-a22a-ddaa80e31626_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business combination, stock conversion ratio</link:label>
    <link:label id="lab_kg_BusinessCombinationStockConversionRatio_label_en-US" xlink:label="lab_kg_BusinessCombinationStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Stock Conversion Ratio</link:label>
    <link:label id="lab_kg_BusinessCombinationStockConversionRatio_documentation_en-US" xlink:label="lab_kg_BusinessCombinationStockConversionRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Stock Conversion Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationStockConversionRatio" xlink:href="kg-20260331.xsd#kg_BusinessCombinationStockConversionRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationStockConversionRatio" xlink:to="lab_kg_BusinessCombinationStockConversionRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_019ce734-5cd9-7a5c-bf21-1fccc30faf3a_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of ceding commission payable, period increase</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceding Commission Payable, Period Increase (Decrease)</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceding Commission Payable, Period Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:to="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ManagementFeeExpense_019ce734-5c52-7e53-afd7-283e43e66eb1_terseLabel_en-US" xlink:label="lab_us-gaap_ManagementFeeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses from related party transactions</link:label>
    <link:label id="lab_us-gaap_ManagementFeeExpense_label_en-US" xlink:label="lab_us-gaap_ManagementFeeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Management Fee Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ManagementFeeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ManagementFeeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ManagementFeeExpense" xlink:to="lab_us-gaap_ManagementFeeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_019ce734-5cd9-7a45-97f0-bc996cafd2d8_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalPeriodFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalPeriodFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Period Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalPeriodFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalPeriodFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalPeriodFocus" xlink:to="lab_dei_DocumentFiscalPeriodFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent_019ce734-5c52-7d83-bc81-48db39b8518b_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, before Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentBeforeTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_019ce734-5c52-716a-b344-e0afd5b7169f_verboseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_019d32fd-b7cb-710e-8fd1-3c92a2aabb93_netLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Intangible assets, net</link:label>
    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_label_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Assets, Net (Including Goodwill)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IntangibleAssetsNetIncludingGoodwill"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:to="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome_019ce734-5c52-7937-9c1c-acd0163c401b_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Accrued investment income</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Accrued Investment Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedInvestmentIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing Method</link:label>
    <link:label id="lab_ecd_AwardTmgMethodTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgMethodTextBlock" xlink:to="lab_ecd_AwardTmgMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_LitigationCaseTypeDomain_019d3d06-b6b1-724b-8f7e-c485c8141d11_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Domain]</link:label>
    <link:label id="lab_srt_LitigationCaseTypeDomain_label_en-US" xlink:label="lab_srt_LitigationCaseTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseTypeDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_LitigationCaseTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseTypeDomain" xlink:to="lab_srt_LitigationCaseTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_019ce734-5ba0-7ed3-8a40-043fd297191f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic loss from continuing operations per share attributable to Kestrel common shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_019ce734-5ba0-7bd7-8c66-1a0f8f609329_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic loss from continuing operations per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Per Basic Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsPerBasicShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsPerBasicShare" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmtrustFinancialServicesIncMember_019ce734-5cd9-78ec-85d1-41745dfe4130_terseLabel_en-US" xlink:label="lab_kg_AmtrustFinancialServicesIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Financial Services, Inc.</link:label>
    <link:label id="lab_kg_AmtrustFinancialServicesIncMember_019ce734-5cd9-75f2-8ef0-13391a30b833_verboseLabel_en-US" xlink:label="lab_kg_AmtrustFinancialServicesIncMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Financial Services, Inc.</link:label>
    <link:label id="lab_kg_AmtrustFinancialServicesIncMember_label_en-US" xlink:label="lab_kg_AmtrustFinancialServicesIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Financial Services, Inc. [Member]</link:label>
    <link:label id="lab_kg_AmtrustFinancialServicesIncMember_documentation_en-US" xlink:label="lab_kg_AmtrustFinancialServicesIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Financial Services, Inc. [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustFinancialServicesIncMember" xlink:href="kg-20260331.xsd#kg_AmtrustFinancialServicesIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmtrustFinancialServicesIncMember" xlink:to="lab_kg_AmtrustFinancialServicesIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_019d33f9-faa8-76ea-b5e6-1148417082ad_terseLabel_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Type</link:label>
    <link:label id="lab_us-gaap_AwardTypeAxis_label_en-US" xlink:label="lab_us-gaap_AwardTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AwardTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AwardTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AwardTypeAxis" xlink:to="lab_us-gaap_AwardTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_019ce734-5cd9-75b6-9ddb-c607db539414_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation</link:label>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Foreign Currency Adjustment Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedTranslationAdjustmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:to="lab_us-gaap_AccumulatedTranslationAdjustmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVenture2Member_019ce734-5cd9-7993-ae15-7de588b46337_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVenture2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Venture 2</link:label>
    <link:label id="lab_kg_SilverstoneVenture2Member_label_en-US" xlink:label="lab_kg_SilverstoneVenture2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture 2 [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVenture2Member_documentation_en-US" xlink:label="lab_kg_SilverstoneVenture2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture2Member" xlink:href="kg-20260331.xsd#kg_SilverstoneVenture2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVenture2Member" xlink:to="lab_kg_SilverstoneVenture2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_019ce734-5ba0-731f-9ca8-a8ddb61a7155_terseLabel_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_label_en-US" xlink:label="lab_srt_EquityMethodInvesteeNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_EquityMethodInvesteeNameDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_EquityMethodInvesteeNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_EquityMethodInvesteeNameDomain" xlink:to="lab_srt_EquityMethodInvesteeNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_019ce734-5c52-7a37-9bd7-2f44b3798fe3_terseLabel_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:label id="lab_dei_TradingSymbol_label_en-US" xlink:label="lab_dei_TradingSymbol" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Symbol</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_TradingSymbol" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_TradingSymbol"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_TradingSymbol" xlink:to="lab_dei_TradingSymbol" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_019ce734-5cd9-7c5b-9caa-74dc23c9277c_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipHeldIndirectlyMember_019df411-5541-7382-b8d5-3b42e076eb07_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Held Indirectly</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldIndirectlyMember_label_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Indirectly [Member]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipHeldIndirectlyMember_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership, Held Indirectly</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:href="kg-20260331.xsd#kg_CommonStockOwnershipHeldIndirectlyMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:to="lab_kg_CommonStockOwnershipHeldIndirectlyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_019ce734-5c52-782b-beed-afe4d0f2e4a6_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Treatment for the Combination</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationsPolicy_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationsPolicy" xlink:to="lab_us-gaap_BusinessCombinationsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_019ce734-5cd9-7131-8209-ce9b1931ae0d_terseLabel_en-US" xlink:label="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of securities in an unrealized loss position</link:label>
    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_label_en-US" xlink:label="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Securities in Unrealized Loss Positions, Qualitative Disclosure, Number of Positions</link:label>
    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_documentation_en-US" xlink:label="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Securities in Unrealized Loss Positions, Qualitative Disclosure, Number of Positions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:href="kg-20260331.xsd#kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:to="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_019ce734-5cd9-74be-b8e0-3bfd01f0b592_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwardsTable_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwardsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwardsTable" xlink:to="lab_us-gaap_OperatingLossCarryforwardsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_019ce734-5cd9-726f-b33a-6752a7e2c19c_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Direct</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredGross" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember_019d33da-9605-76a8-a1ee-3601bd51c7bb_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBITDA &amp; Commission Equity Volatility Rate</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember_label_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Volatility Rate [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Volatility Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:href="kg-20260331.xsd#kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:to="lab_kg_MeasurementInputEBITDAAndCommissionVolatilityRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019ce734-5c52-727d-bbc8-8e65a7f159ac_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities (includes $27,468 and $16,443 from related parties in 2026 and 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_019ce734-5c52-780d-bad5-1bc9d5d3d54c_verboseLabel_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities_label_en-US" xlink:label="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Liabilities and Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedLiabilitiesAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:to="lab_us-gaap_AccruedLiabilitiesAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_019ce734-5c52-7df0-bf77-5ceb85b56938_terseLabel_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of unrealized loss positions</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_label_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_documentation_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:href="kg-20260331.xsd#kg_InvestmentsContinuousUnrealizedLossPositionFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:to="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCityOrTown_019ce734-5cd9-721f-a06f-3c7e5d31d3c9_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:label id="lab_dei_EntityAddressCityOrTown_label_en-US" xlink:label="lab_dei_EntityAddressCityOrTown" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, City or Town</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCityOrTown" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCityOrTown"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCityOrTown" xlink:to="lab_dei_EntityAddressCityOrTown" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ce734-5cd9-7424-8e11-401d477fde79_terseLabel_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of exchange rate changes on foreign currency cash, restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effect of Exchange Rate on Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:to="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:label id="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt_label_en-US" xlink:label="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO Average Compensation Actually Paid Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoAvgCompActuallyPaidAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:to="lab_ecd_NonPeoNeoAvgCompActuallyPaidAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_019ddf7f-97a7-7da4-96d8-cfe02d7dad57_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationDomain_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationDomain" xlink:to="lab_us-gaap_IncomeStatementLocationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Other Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsOtherMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsOtherMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019ce734-5ba1-7a05-a25a-3dc9b0ad51d2_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total consideration effectively transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_019ce734-5ba1-7eb1-a2e1-d7c5bd7b4bfc_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total consideration effectively transferred</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferred1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferred1" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_019ce734-5cd9-7885-9ba3-0ff226c94f3c_terseLabel_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:label id="lab_dei_EntityEmergingGrowthCompany_label_en-US" xlink:label="lab_dei_EntityEmergingGrowthCompany" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Emerging Growth Company</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityEmergingGrowthCompany" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityEmergingGrowthCompany"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityEmergingGrowthCompany" xlink:to="lab_dei_EntityEmergingGrowthCompany" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_019ce734-5c52-7b16-8e62-e7f5575a001e_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in assets &#8211; (increase) decrease:</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingAssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingAssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year</link:label>
    <link:label id="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Change in Fair Value as of Vesting Date of Prior Year Equity Awards Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:to="lab_ecd_ChngInFrValAsOfVstngDtOfPrrYrEqtyAwrdsVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_019ce734-5c52-77d9-bf71-9939461cc7e3_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: unamortized fair value adjustment</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsNet_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsNet" xlink:to="lab_us-gaap_DeferredFinanceCostsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_019ce734-5cd9-790f-bdc9-3156d99c17c6_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_019ce734-5cd9-78e4-ae50-13d4b1c4a60b_netLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Restricted cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_019ce734-5cd9-73f1-a07a-6fe4abfc174c_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total restricted cash</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndCashEquivalents" xlink:to="lab_us-gaap_RestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_019ce734-5cd9-70a5-836c-3eff09fb4316_terseLabel_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diversified Legacy Reinsurance</link:label>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_019ce734-5cd9-7819-8bbf-a4eb6ef87b3b_verboseLabel_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance legacy business</link:label>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Diversified Reinsurance Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiversifiedReinsuranceSegmentMember" xlink:href="kg-20260331.xsd#kg_DiversifiedReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DiversifiedReinsuranceSegmentMember" xlink:to="lab_kg_DiversifiedReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_019ce734-5c52-7d2f-b291-473050cbe695_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, outstanding (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesOutstanding" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesOutstanding" xlink:to="lab_us-gaap_CommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InsuranceAbstract_019ce734-5ba0-765d-888e-23f78a38ab2f_terseLabel_en-US" xlink:label="lab_us-gaap_InsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance [Abstract]</link:label>
    <link:label id="lab_us-gaap_InsuranceAbstract_label_en-US" xlink:label="lab_us-gaap_InsuranceAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InsuranceAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InsuranceAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InsuranceAbstract" xlink:to="lab_us-gaap_InsuranceAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy_019ce734-5cd9-7452-8286-d5dc50b0f355_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance, amount retained, per policy</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Amount Retained, Per Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:to="lab_us-gaap_ReinsuranceRetentionAmountRetainedPerPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GLSToRPPMember_019d3d06-b6b1-7461-adeb-0092c83763cc_terseLabel_en-US" xlink:label="lab_kg_GLSToRPPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GLS to RPP</link:label>
    <link:label id="lab_kg_GLSToRPPMember_label_en-US" xlink:label="lab_kg_GLSToRPPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GLS to RPP [Member]</link:label>
    <link:label id="lab_kg_GLSToRPPMember_documentation_en-US" xlink:label="lab_kg_GLSToRPPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GLS to RPP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GLSToRPPMember" xlink:href="kg-20260331.xsd#kg_GLSToRPPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GLSToRPPMember" xlink:to="lab_kg_GLSToRPPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_019ce734-5c52-77f5-a685-adfda1d6e752_terseLabel_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments transferred out related to Partial Termination Amendment and Commutation</link:label>
    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_label_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Quota Shares Reinsurance Agreement, Partial Termination Amendment [Member]</link:label>
    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_documentation_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Quota Shares Reinsurance Agreement, Partial Termination Amendment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:href="kg-20260331.xsd#kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:to="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_019ce734-5ba0-7c39-980a-a0cd667ba90c_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares from vesting of stock based compensation</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Stock Options Exercised</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:to="lab_us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year</link:label>
    <link:label id="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember_label_en-US" xlink:label="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends or Other Earnings Paid on Equity Awards not Otherwise Reflected in Total Compensation for Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:to="lab_ecd_DvddsOrOthrErngsPdOnEqtyAwrdsNtOthrwsRflctdInTtlCompForCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_019d3d34-d556-7852-8b41-0e30f9e2e560_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Estimated Aggregate Amortization Expense</link:label>
    <link:label id="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Finite-Lived Intangible Assets, Future Amortization Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:to="lab_us-gaap_ScheduleofFiniteLivedIntangibleAssetsFutureAmortizationExpenseTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities_019ce734-5ba0-705a-ab51-bbc29ae0f902_terseLabel_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, available-for-sale, at fair value</link:label>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities_label_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Including Discontinued Operation, Debt Securities</link:label>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities_documentation_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group Including Discontinued Operation, Debt Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities" xlink:href="kg-20260331.xsd#kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities" xlink:to="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_019ce734-5cd9-7bfd-b707-fe2ae618f39f_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares issued or to be issued (in shares)</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_label_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Shares issued or To Be Issued</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_documentation_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Shares issued or To Be Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:href="kg-20260331.xsd#kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:to="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_019ce734-5c52-7aa9-a331-fb1dd0a5cbd0_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Effective Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateEffectivePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateEffectivePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressPostalZipCode_019ce734-5cd9-7042-88f8-9c8245fc8083_terseLabel_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:label id="lab_dei_EntityAddressPostalZipCode_label_en-US" xlink:label="lab_dei_EntityAddressPostalZipCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Postal Zip Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressPostalZipCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressPostalZipCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressPostalZipCode" xlink:to="lab_dei_EntityAddressPostalZipCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDeterminationDate_terseLabel_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:label id="lab_ecd_RestatementDeterminationDate_label_en-US" xlink:label="lab_ecd_RestatementDeterminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDeterminationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDeterminationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDeterminationDate" xlink:to="lab_ecd_RestatementDeterminationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019ce734-5cd9-792e-a8f0-7a715ff7304a_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019ce734-5cd9-789b-a8f0-8711a92e9480_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_019ce734-5cd9-7a9f-9b45-41edeb67025b_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_019ce734-5c52-71aa-bba7-db47b6e2e960_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fed funds rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Basis Spread on Variable Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentBasisSpreadOnVariableRate1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:to="lab_us-gaap_DebtInstrumentBasisSpreadOnVariableRate1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_019ce734-5ba0-7c21-b434-a53886029f2d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basic loss from discontinued operations per share attributable to Kestrel common shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_019ce734-5ba0-7c90-9193-a81a4da05559_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Basic loss from discontinued operations per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Basic Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:to="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerBasicShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherAssets_019ce734-5c52-733e-8c7b-52d389cc8e31_terseLabel_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_OtherAssets_label_en-US" xlink:label="lab_us-gaap_OtherAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherAssets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherAssets" xlink:to="lab_us-gaap_OtherAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019ce734-5c52-738c-adea-378fe3a36d0a_periodStartLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Balance - beginning of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_019ce734-5c52-776a-97a0-eb2fe8c16174_periodEndLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Total Level 3 investments - end of period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_CreditRatingStandardPoorsAxis_019ce734-5cd9-7785-86ff-d914d4ddf15e_terseLabel_en-US" xlink:label="lab_srt_CreditRatingStandardPoorsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Rating, Standard &amp; Poor's [Axis]</link:label>
    <link:label id="lab_srt_CreditRatingStandardPoorsAxis_label_en-US" xlink:label="lab_srt_CreditRatingStandardPoorsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Rating, Standard &amp; Poor's [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_CreditRatingStandardPoorsAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_CreditRatingStandardPoorsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_CreditRatingStandardPoorsAxis" xlink:to="lab_srt_CreditRatingStandardPoorsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsSvcCstMember" xlink:to="lab_ecd_PnsnAdjsSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_019ce734-5c52-72e8-ad41-58a98ff1048d_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:label id="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis_label_en-US" xlink:label="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueByFairValueHierarchyLevelAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:to="lab_us-gaap_FairValueByFairValueHierarchyLevelAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember_019ce734-5c52-7127-ad9b-24ecc0f08122_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Held-for-sale</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Held-for-Sale [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsHeldforsaleMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:to="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_019ce734-5c52-7a98-bd0d-212d66e186bd_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations and Disposal Groups [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:to="lab_us-gaap_DiscontinuedOperationsAndDisposalGroupsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentManagementFeesMember_019ce734-5ba0-7c70-92ea-d39455ab1e15_terseLabel_en-US" xlink:label="lab_kg_InvestmentManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Management Fee</link:label>
    <link:label id="lab_kg_InvestmentManagementFeesMember_label_en-US" xlink:label="lab_kg_InvestmentManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Management Fees [Member]</link:label>
    <link:label id="lab_kg_InvestmentManagementFeesMember_documentation_en-US" xlink:label="lab_kg_InvestmentManagementFeesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Management Fees [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentManagementFeesMember" xlink:href="kg-20260331.xsd#kg_InvestmentManagementFeesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentManagementFeesMember" xlink:to="lab_kg_InvestmentManagementFeesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Company Selected Measure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsCoSelectedMeasureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionSolvencyRatio_019ce734-5cd9-726e-9974-92dc2e0ceb5a_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Solvency ratio</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionSolvencyRatio_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Solvency Ratio</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionSolvencyRatio_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Solvency Ratio</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionSolvencyRatio" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionSolvencyRatio"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionSolvencyRatio" xlink:to="lab_kg_RelatedPartyTransactionSolvencyRatio" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllTradingArrangementsMember_terseLabel_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Trading Arrangements</link:label>
    <link:label id="lab_ecd_AllTradingArrangementsMember_label_en-US" xlink:label="lab_ecd_AllTradingArrangementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Trading Arrangements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllTradingArrangementsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllTradingArrangementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllTradingArrangementsMember" xlink:to="lab_ecd_AllTradingArrangementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjFnTextBlock" xlink:to="lab_ecd_EqtyAwrdsAdjFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Vs Peer Group [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnVsPeerGroupTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:to="lab_ecd_TotalShareholderRtnVsPeerGroupTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_019ce734-5c52-7705-b965-8edafb6e9f49_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Redemption price, percentage</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Redemption Price, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentRedemptionPricePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:to="lab_us-gaap_DebtInstrumentRedemptionPricePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_019ce734-5ba1-7435-b180-4bd6f2c337c2_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral held by related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Collateral Held by Related Party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Collateral Held by Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionCollateralHeldByRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfDirectorsSelectedByAffiliate_019ce734-5c52-7e6b-b7c1-32464b6fb1f7_terseLabel_en-US" xlink:label="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of directors, selected by affiliate</link:label>
    <link:label id="lab_kg_NumberOfDirectorsSelectedByAffiliate_label_en-US" xlink:label="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Directors, Selected by Affiliate</link:label>
    <link:label id="lab_kg_NumberOfDirectorsSelectedByAffiliate_documentation_en-US" xlink:label="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Directors, Selected by Affiliate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectorsSelectedByAffiliate" xlink:href="kg-20260331.xsd#kg_NumberOfDirectorsSelectedByAffiliate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfDirectorsSelectedByAffiliate" xlink:to="lab_kg_NumberOfDirectorsSelectedByAffiliate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_019ce734-5c52-7996-baca-99675d3aa0c1_negatedLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Senior notes - at fair value</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Long-Term Debt</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_019ce734-5c52-74c6-80d4-fd2f6dec143b_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral on exposure</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Collateral On Exposure</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Collateral On Exposure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentageOfCollateralOnExposure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:to="lab_kg_RelatedPartyTransactionPercentageOfCollateralOnExposure" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_019ce734-5c52-768c-bf13-f2df00fb3899_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingenciesDisclosureAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:to="lab_us-gaap_CommitmentsAndContingenciesDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount_019dfe5d-eb38-7c72-8125-09a8fdb82b85_terseLabel_en-US" xlink:label="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated recovery amount, maximum</link:label>
    <link:label id="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount_label_en-US" xlink:label="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Contingency, Estimated Recovery from Third Party, Amount</link:label>
    <link:label id="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount_documentation_en-US" xlink:label="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain Contingency, Estimated Recovery from Third Party, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount" xlink:href="kg-20260331.xsd#kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount" xlink:to="lab_kg_GainContingencyEstimatedRecoveryFromThirdPartyAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromInsurancePremiumsCollected_019d3d06-b6b1-79a7-8532-35c578ffd5b7_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromInsurancePremiumsCollected" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from insurance premiums collected</link:label>
    <link:label id="lab_us-gaap_ProceedsFromInsurancePremiumsCollected_label_en-US" xlink:label="lab_us-gaap_ProceedsFromInsurancePremiumsCollected" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Insurance Premiums Collected</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromInsurancePremiumsCollected" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromInsurancePremiumsCollected"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromInsurancePremiumsCollected" xlink:to="lab_us-gaap_ProceedsFromInsurancePremiumsCollected" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_019ce734-5c52-7485-b490-4eff1ded4635_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_019ce734-5c52-7424-b8c4-f4a553d3345f_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sales of fixed maturities&#160;</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale of Debt Securities, Available-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:to="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery_019ce734-5c52-7837-b1a5-84c955f3407a_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Increase in allowance for expected credit losses on reinsurance recoverable where credit losses were previously recognized</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss, Recovery</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery" xlink:to="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRecovery" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_019ce734-5ba0-7ca6-ae1c-9661143bd61b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Sales</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Sales</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetSales" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_019ce734-5cd9-7679-844c-a2ea2017188f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Other Asset, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_019ce734-5cd9-7824-9f47-e007fa4565ea_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote</link:label>
    <link:label id="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock_label_en-US" xlink:label="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Valuation Assumption Difference, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EquityValuationAssumptionDifferenceFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:to="lab_ecd_EquityValuationAssumptionDifferenceFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoTotalCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoTotalCompAmt_label_en-US" xlink:label="lab_ecd_PeoTotalCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Total Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoTotalCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoTotalCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoTotalCompAmt" xlink:to="lab_ecd_PeoTotalCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_019ce734-5c52-7d73-babc-6e0528b6a3ee_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Axis]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeAxis_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeAxis" xlink:to="lab_us-gaap_LongtermDebtTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_019ce734-5c52-7c10-ae8d-6df37cb17d46_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underwriting-related derivative liability, measurement inputs</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityMeasurementInput_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityMeasurementInput" xlink:to="lab_us-gaap_DerivativeLiabilityMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LossContingencyAggregateCoverageAmount_019d3d06-b6b1-7a46-b23a-288ccaf58cf1_terseLabel_en-US" xlink:label="lab_kg_LossContingencyAggregateCoverageAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss contingency, aggregate coverage amount</link:label>
    <link:label id="lab_kg_LossContingencyAggregateCoverageAmount_label_en-US" xlink:label="lab_kg_LossContingencyAggregateCoverageAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Aggregate Coverage Amount</link:label>
    <link:label id="lab_kg_LossContingencyAggregateCoverageAmount_documentation_en-US" xlink:label="lab_kg_LossContingencyAggregateCoverageAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency, Aggregate Coverage Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LossContingencyAggregateCoverageAmount" xlink:href="kg-20260331.xsd#kg_LossContingencyAggregateCoverageAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LossContingencyAggregateCoverageAmount" xlink:to="lab_kg_LossContingencyAggregateCoverageAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_019d3d3a-b9f3-70cf-85c9-5817e5d7767a_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseRemainderOfFiscalYear" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_019ce734-5ba0-722e-a26a-7d0e4be661cb_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Denominator:</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:to="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsAbstract_019ce734-5ba0-7a74-87a3-1bd5a8a20c99_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Abstract]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsAbstract" xlink:to="lab_us-gaap_ScheduleOfInvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_019ce734-5ba0-7fc6-a164-5849d931f0b8_terseLabel_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementEquityComponentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementEquityComponentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Components [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementEquityComponentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementEquityComponentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementEquityComponentsAxis" xlink:to="lab_us-gaap_StatementEquityComponentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax_019ce734-5c52-7630-8ce7-ad1dfff02f50_terseLabel_en-US" xlink:label="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized losses on held for sale AFS fixed maturities</link:label>
    <link:label id="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax_label_en-US" xlink:label="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Held-for-Sale, Unrealized Holding Gain (Loss), before Adjustment and Tax</link:label>
    <link:label id="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax_documentation_en-US" xlink:label="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Held-for-Sale, Unrealized Holding Gain (Loss), before Adjustment and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax" xlink:href="kg-20260331.xsd#kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax"/>
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    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_NonRule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonRule10b51ArrAdoptedFlag"/>
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    <link:label id="lab_us-gaap_NumberOfReportableSegments_019ce734-5cd9-77d2-942c-69720ec043d2_terseLabel_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reporting segments</link:label>
    <link:label id="lab_us-gaap_NumberOfReportableSegments_label_en-US" xlink:label="lab_us-gaap_NumberOfReportableSegments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Reportable Segments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NumberOfReportableSegments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NumberOfReportableSegments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NumberOfReportableSegments" xlink:to="lab_us-gaap_NumberOfReportableSegments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansPayable_019ce734-5c52-7f7f-b473-03647745bee0_terseLabel_en-US" xlink:label="lab_us-gaap_LoansPayable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance principal amount</link:label>
    <link:label id="lab_us-gaap_LoansPayable_label_en-US" xlink:label="lab_us-gaap_LoansPayable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans Payable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansPayable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansPayable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansPayable" xlink:to="lab_us-gaap_LoansPayable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019ce734-5ba0-735c-908e-dcdfbb9142d0_terseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019ce734-5ba0-72d6-a9af-36b5f2b673ff_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019ce734-5ba0-7424-8db4-a8eb1efaad9a_totalLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_019ce734-5ba0-7be7-a243-09db0e95e867_negatedLabel_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE</link:label>
    <link:label id="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_label_en-US" xlink:label="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PolicyholderBenefitsAndClaimsIncurredNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:to="lab_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressCountry_019ce734-5c52-7cde-96de-e4aebaca935d_terseLabel_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:label id="lab_dei_EntityAddressCountry_label_en-US" xlink:label="lab_dei_EntityAddressCountry" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Country</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressCountry" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressCountry"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressCountry" xlink:to="lab_dei_EntityAddressCountry" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_019d3d1e-ade1-78e0-8063-ec8d126d19d9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:to="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_IndividualAxis_terseLabel_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Individual:</link:label>
    <link:label id="lab_ecd_IndividualAxis_label_en-US" xlink:label="lab_ecd_IndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Individual [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_IndividualAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_IndividualAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_IndividualAxis" xlink:to="lab_ecd_IndividualAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member_019d33da-9605-7a4b-a4cc-5566a6dfd1ab_verboseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 1</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 1 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 1</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyTable_019ce734-5c52-798f-9101-1cdf6e26410b_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Retention Policy [Table]</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyTable_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Retention [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionPolicyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyTable" xlink:to="lab_us-gaap_ReinsuranceRetentionPolicyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_019ce734-5cd9-7c2f-b7cd-a338b6038fbb_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Domain]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityDomain"/>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments_019ce734-5c52-7103-a9bf-429a00e36c73_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Equity Method Investments</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments"/>
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    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_019ce734-5cd9-775f-b0ed-5dc839e23bd2_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquisition option term</link:label>
    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_label_en-US" xlink:label="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Option Term</link:label>
    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_documentation_en-US" xlink:label="lab_kg_BusinessCombinationAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Acquisition Option Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationAcquisitionOptionTerm" xlink:href="kg-20260331.xsd#kg_BusinessCombinationAcquisitionOptionTerm"/>
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    <link:label id="lab_kg_OtherInvestmentMember_019ce734-5c52-728d-96e5-1b310e83df10_terseLabel_en-US" xlink:label="lab_kg_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_kg_OtherInvestmentMember_label_en-US" xlink:label="lab_kg_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investment [Member]</link:label>
    <link:label id="lab_kg_OtherInvestmentMember_documentation_en-US" xlink:label="lab_kg_OtherInvestmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentMember" xlink:href="kg-20260331.xsd#kg_OtherInvestmentMember"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_019ce734-5c52-7190-bba9-97b678b7e2ed_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost of securities without single maturities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, without Single Maturity Date, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost"/>
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    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability [Text Block]</link:label>
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    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_019ce734-5ba0-7dd9-9756-084d6bc4d627_terseLabel_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minority interest</link:label>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_label_en-US" xlink:label="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Subsidiary, Ownership Percentage, Noncontrolling Owner</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:to="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_019ce734-5c52-7d02-a6bc-9a7176894382_terseLabel_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:label id="lab_dei_EntityInteractiveDataCurrent_label_en-US" xlink:label="lab_dei_EntityInteractiveDataCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Interactive Data Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityInteractiveDataCurrent" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityInteractiveDataCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityInteractiveDataCurrent" xlink:to="lab_dei_EntityInteractiveDataCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_019ce734-5c52-70c6-affd-b9e7ba7e3cbb_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Other Investments</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_019ce734-5cd9-7b37-a3b8-92711e1990e3_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Net Loan Receivable From Related Party</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Net Loan Receivable From Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_019ce734-5c52-7f94-afd8-bc6f613075da_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, available-for-sale, at fair value</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Fixed Maturities, Available For Sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Fixed Maturities, Available For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeAxis_019ce734-5ba0-7232-aca4-6a4c911bd551_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Axis]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeAxis_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Axis]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeAxis_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeAxis" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionByTypeAxis" xlink:to="lab_kg_RelatedPartyTransactionByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_OwnershipDomain_019ce734-5c52-7757-a232-04b6fbfe5a1e_terseLabel_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:label id="lab_srt_OwnershipDomain_label_en-US" xlink:label="lab_srt_OwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_OwnershipDomain" xlink:to="lab_srt_OwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_019ce734-5c52-76ef-a409-a2af6ca93f9f_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Portion of the Maiden awards attributable to pre-combination service</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Consideration Transferred Attributable to Pre Combination Service</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Consideration Transferred Attributable to Pre Combination Service</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:href="kg-20260331.xsd#kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestPayableCurrent_019ce734-5ba0-7e30-88d1-cb0fb492258f_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest</link:label>
    <link:label id="lab_us-gaap_InterestPayableCurrent_label_en-US" xlink:label="lab_us-gaap_InterestPayableCurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Payable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPayableCurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPayableCurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPayableCurrent" xlink:to="lab_us-gaap_InterestPayableCurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCentralIndexKey_019ce734-5ba0-7916-af1a-48101fbe7f0c_terseLabel_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:label id="lab_dei_EntityCentralIndexKey_label_en-US" xlink:label="lab_dei_EntityCentralIndexKey" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Central Index Key</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCentralIndexKey" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCentralIndexKey"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCentralIndexKey" xlink:to="lab_dei_EntityCentralIndexKey" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoName_terseLabel_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:label id="lab_ecd_PeoName_label_en-US" xlink:label="lab_ecd_PeoName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoName" xlink:to="lab_ecd_PeoName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Revenues_019ce734-5c52-742c-8403-6e9baefd3947_totalLabel_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_Revenues_label_en-US" xlink:label="lab_us-gaap_Revenues" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Revenues" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Revenues"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Revenues" xlink:to="lab_us-gaap_Revenues" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year</link:label>
    <link:label id="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember_label_en-US" xlink:label="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year End Fair Value of Equity Awards Granted in Any Prior Year that Fail to Meet Applicable Vesting Conditions During Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:to="lab_ecd_FrValAsOfPrrYrEndOfEqtyAwrdsGrntdInPrrYrsFldVstngCondsDrngCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingAggtErrCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingAggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingAggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingAggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingAggtErrCompAmt" xlink:to="lab_ecd_OutstandingAggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_019ce734-5c52-752c-879e-edf63e05c6e4_totalLabel_en-US" xlink:label="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized gains (losses) on investment, gross gains</link:label>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_label_en-US" xlink:label="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Gain On Investments</link:label>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_documentation_en-US" xlink:label="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Gain On Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealizedAndUnrealizedGainOnInvestments" xlink:href="kg-20260331.xsd#kg_RealizedAndUnrealizedGainOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RealizedAndUnrealizedGainOnInvestments" xlink:to="lab_kg_RealizedAndUnrealizedGainOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_019ce734-5ba0-7c68-8a98-630f2c68eb42_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:to="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_019ce734-5c52-7a08-b089-afb574ac9e54_terseLabel_en-US" xlink:label="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Quota Share Reinsurance Agreements</link:label>
    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_label_en-US" xlink:label="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Quota Share Reinsurance Agreements [Member]</link:label>
    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_documentation_en-US" xlink:label="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Quota Share Reinsurance Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_QuotaShareReinsuranceAgreementsMember" xlink:href="kg-20260331.xsd#kg_QuotaShareReinsuranceAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_QuotaShareReinsuranceAgreementsMember" xlink:to="lab_kg_QuotaShareReinsuranceAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019ce734-5cd9-7b08-b4ff-7e5579c12416_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019ce734-5cd9-7224-8e7b-8d3a137efa53_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019ce734-5cd9-7469-bb6a-627c20dff0d8_netLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_019ce734-5cd9-7ec0-beaf-968d13674a16_totalLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenNet_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsWrittenNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsWrittenNet" xlink:to="lab_us-gaap_PremiumsWrittenNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_019ce734-5c52-77fe-89a2-03ffd8cd7791_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net, allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_label_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Receivable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:to="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardExrcPrice_terseLabel_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Exercise Price</link:label>
    <link:label id="lab_ecd_AwardExrcPrice_label_en-US" xlink:label="lab_ecd_AwardExrcPrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardExrcPrice" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardExrcPrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardExrcPrice" xlink:to="lab_ecd_AwardExrcPrice" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityFilerCategory_019ce734-5cd9-75ee-9bb7-cd43e167322a_terseLabel_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:label id="lab_dei_EntityFilerCategory_label_en-US" xlink:label="lab_dei_EntityFilerCategory" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Filer Category</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityFilerCategory" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityFilerCategory"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityFilerCategory" xlink:to="lab_dei_EntityFilerCategory" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale_019ce734-5c52-7921-8387-4b08b66ef655_terseLabel_en-US" xlink:label="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less: change in cash and cash equivalents held for sale</link:label>
    <link:label id="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale_label_en-US" xlink:label="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Held-for-Sale</link:label>
    <link:label id="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale_documentation_en-US" xlink:label="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Cash, Cash Equivalents, Restricted Cash, and Restricted Cash Equivalents, Held-for-Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale" xlink:href="kg-20260331.xsd#kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale" xlink:to="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DirectLendingEntitiesMember_019ce734-5cd9-7233-b84d-e53b23e45139_terseLabel_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments in direct lending entities</link:label>
    <link:label id="lab_kg_DirectLendingEntitiesMember_label_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Lending Entities [Member]</link:label>
    <link:label id="lab_kg_DirectLendingEntitiesMember_documentation_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Direct Lending Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DirectLendingEntitiesMember" xlink:href="kg-20260331.xsd#kg_DirectLendingEntitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DirectLendingEntitiesMember" xlink:to="lab_kg_DirectLendingEntitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019d3d3a-b9f3-7d2b-8656-52d1032bb92d_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_019ce734-5ba0-73ab-87cb-4633d03f68e4_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Cash and Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_terseLabel_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year</link:label>
    <link:label id="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember_label_en-US" xlink:label="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting Date Fair Value of Equity Awards Granted and Vested in Covered Year [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:to="lab_ecd_VstngDtFrValOfEqtyAwrdsGrntdAndVstdInCvrdYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_019ce734-5cd9-7c88-9867-1a6f0b18b04d_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_019ce734-5cd9-75c5-a7c3-65c06712ef10_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Gross premiums written</link:label>
    <link:label id="lab_us-gaap_PremiumsWrittenGross_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsWrittenGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsWrittenGross" xlink:to="lab_us-gaap_PremiumsWrittenGross" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityAddressAddressLine1_019ce734-5cd9-7128-b200-a05ad7462021_terseLabel_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:label id="lab_dei_EntityAddressAddressLine1_label_en-US" xlink:label="lab_dei_EntityAddressAddressLine1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Address, Address Line One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityAddressAddressLine1" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityAddressAddressLine1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityAddressAddressLine1" xlink:to="lab_dei_EntityAddressAddressLine1" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentUnrealizedGainLoss_019ce734-5c52-7050-b85f-190bada9d5d3_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized losses on held for sale AFS investments</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentUnrealizedGainLoss_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Unrealized Gain (Loss)</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentUnrealizedGainLoss_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentUnrealizedGainLoss" xlink:href="kg-20260331.xsd#kg_EquityMethodInvestmentUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquityMethodInvestmentUnrealizedGainLoss" xlink:to="lab_kg_EquityMethodInvestmentUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019ce734-5ba0-72fc-ae98-5ad0ec8de629_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_019ce734-5ba0-7624-938d-a5052d36d88a_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI Attributable to Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_019ce734-5cd9-7ab9-a6ad-05880cac2576_verboseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Liabilities and Other Operating Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:to="lab_us-gaap_IncreaseDecreaseInAccruedLiabilitiesAndOtherOperatingLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_019ce734-5c52-70c3-b7af-38e40d759b66_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeCategorizationMember_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeCategorizationMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeCategorizationMember" xlink:to="lab_us-gaap_InvestmentTypeCategorizationMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_019ce734-5cd9-7b0b-922c-3a7a2bb4deda_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses: (Allowance for expected credit losses: 2026: $1,930; 2025: $1,740)</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_019ce734-5cd9-7501-a85f-6ff5c00eb14e_verboseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable for Unpaid Claims and Claims Adjustments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:to="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_019ce734-5ba0-7c0e-a376-4a4fb1c526f4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Asset Acquisition, Transaction between Entities under Common Control, and Joint Venture Formation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationAndAssetAcquisitionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationAndAssetAcquisitionAbstract"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_019ce734-5ba0-7ea2-b895-cc5ef1cf91d4_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
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    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote</link:label>
    <link:label id="lab_ecd_AdjToPeoCompFnTextBlock_label_en-US" xlink:label="lab_ecd_AdjToPeoCompFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment To PEO Compensation, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AdjToPeoCompFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AdjToPeoCompFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AdjToPeoCompFnTextBlock" xlink:to="lab_ecd_AdjToPeoCompFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_019ce734-5c52-72fe-b1a1-f977d59ff9a1_terseLabel_en-US" xlink:label="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_label_en-US" xlink:label="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accrued Investment Income Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccruedInvestmentIncomeReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccruedInvestmentIncomeReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccruedInvestmentIncomeReceivable" xlink:to="lab_us-gaap_AccruedInvestmentIncomeReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_019ce734-5c52-71b3-b2ab-0a72b68b87e8_terseLabel_en-US" xlink:label="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards, with no expiry date, percentage</link:label>
    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_label_en-US" xlink:label="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration, Percentage</link:label>
    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_documentation_en-US" xlink:label="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Not Subject to Expiration, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage" xlink:href="kg-20260331.xsd#kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage"/>
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    <link:label id="lab_us-gaap_InvestmentTypeAxis_019ce734-5c52-7685-b0a7-495378dacdec_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeAxis_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentTypeAxis" xlink:to="lab_us-gaap_InvestmentTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Investments_019ce734-5cd9-7ff9-9b27-9ecf2a3a7680_totalLabel_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investments</link:label>
    <link:label id="lab_us-gaap_Investments_label_en-US" xlink:label="lab_us-gaap_Investments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Investments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Investments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Investments" xlink:to="lab_us-gaap_Investments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndTitle_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title</link:label>
    <link:label id="lab_ecd_TrdArrIndTitle_label_en-US" xlink:label="lab_ecd_TrdArrIndTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Title</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndTitle" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndTitle" xlink:to="lab_ecd_TrdArrIndTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_PeerGroupTotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupTotalShareholderRtnAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupTotalShareholderRtnAmt" xlink:to="lab_ecd_PeerGroupTotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment_019ce734-5cd9-7623-8944-cf73bf0a4f46_terseLabel_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effect of foreign exchange rate movements</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment_label_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Foreign Currency Transaction and Translation Adjustment</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment_documentation_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Increase (decrease) in liability for unpaid claims and claims adjustment expense due to foreign currency transaction and translation adjustments.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:href="kg-20260331.xsd#kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:to="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseForeignCurrencyTransactionAndTranslationAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_019ce734-5ba0-799b-afff-df988b04392a_totalLabel_en-US" xlink:label="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other investments, net</link:label>
    <link:label id="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_label_en-US" xlink:label="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Other Securities, Excluding Debt and Equity Securities</link:label>
    <link:label id="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities_documentation_en-US" xlink:label="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Other Securities, Excluding Debt and Equity Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:href="kg-20260331.xsd#kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:to="lab_kg_GainLossOnOtherSecuritiesExcludingDebtAndEquitySecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock_019ce734-5c52-786b-9af6-5b7ee6af8853_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of the Credit Ratings of Fixed Maturities</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock_label_en-US" xlink:label="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investment Credit Ratings [Table Text Block]</link:label>
    <link:label id="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock_documentation_en-US" xlink:label="lab_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Investment Credit Ratings [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfInvestmentCreditRatingsTableTextBlock" xlink:href="kg-20260331.xsd#kg_ScheduleOfInvestmentCreditRatingsTableTextBlock"/>
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    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019ce734-5c52-7403-99f6-3612dc789571_negatedLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Total PPD for Legacy Reinsurance Segment</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019ce734-5c52-775a-b5bb-10907c4c5ba6_terseLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total AmTrust Reinsurance PPD</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019ce734-5c52-7eca-8d29-2af52ce249ad_negatedTerseLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Total AmTrust Reinsurance PPD</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_label_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Period Increase (Decrease), Net of Commission Changes</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_documentation_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Period Increase (Decrease), Net of Commission Changes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:href="kg-20260331.xsd#kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_019ce734-5ba1-71e5-851a-dfcc370ad4af_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Upfront cash</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireBusinessesGross_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Businesses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireBusinessesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireBusinessesGross" xlink:to="lab_us-gaap_PaymentsToAcquireBusinessesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsNetUnrealizedGainLoss_019ce734-5c52-7c72-ac87-b86e83c9058b_terseLabel_en-US" xlink:label="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains on fixed maturity investments</link:label>
    <link:label id="lab_kg_InvestmentsNetUnrealizedGainLoss_label_en-US" xlink:label="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Net Unrealized Gain (Loss)</link:label>
    <link:label id="lab_kg_InvestmentsNetUnrealizedGainLoss_documentation_en-US" xlink:label="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Net Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsNetUnrealizedGainLoss" xlink:href="kg-20260331.xsd#kg_InvestmentsNetUnrealizedGainLoss"/>
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    <link:label id="lab_ecd_NonPeoNeoMember_terseLabel_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-PEO NEO</link:label>
    <link:label id="lab_ecd_NonPeoNeoMember_label_en-US" xlink:label="lab_ecd_NonPeoNeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-PEO NEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_NonPeoNeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_NonPeoNeoMember"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_019ce734-5c52-774f-a6f1-da830f4754cb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_019ce734-5ba0-7dfb-b67c-2a2f2ef45b76_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards expire</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Operating Loss Carryforwards, Subject to Expiration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FeeIncome_019ce734-5c52-7af3-91aa-41d92fcc772e_terseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fee revenue</link:label>
    <link:label id="lab_us-gaap_FeeIncome_019ce734-5c52-712e-b869-61e6308f9961_verboseLabel_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fee revenue</link:label>
    <link:label id="lab_us-gaap_FeeIncome_label_en-US" xlink:label="lab_us-gaap_FeeIncome" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fee Income</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FeeIncome" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FeeIncome"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FeeIncome" xlink:to="lab_us-gaap_FeeIncome" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GenesisLegacySolutionsMember_019ce734-5c52-7626-bd94-bee4d22e8210_terseLabel_en-US" xlink:label="lab_kg_GenesisLegacySolutionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Genesis Legacy Solutions</link:label>
    <link:label id="lab_kg_GenesisLegacySolutionsMember_label_en-US" xlink:label="lab_kg_GenesisLegacySolutionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Genesis Legacy Solutions [Member]</link:label>
    <link:label id="lab_kg_GenesisLegacySolutionsMember_documentation_en-US" xlink:label="lab_kg_GenesisLegacySolutionsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Genesis Legacy Solutions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GenesisLegacySolutionsMember" xlink:href="kg-20260331.xsd#kg_GenesisLegacySolutionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GenesisLegacySolutionsMember" xlink:to="lab_kg_GenesisLegacySolutionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_019ce734-5ba0-75f3-bff9-ae9bcfc5f4b1_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_019ce734-5c52-77d4-9aa2-9e2b98e1152d_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross unrealized gains</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract_019d3d3d-27cb-7459-8027-a5412cd149fa_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Identifiable Intangible Asset, Excluding Goodwill [Abstract]</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwillAbstract"/>
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    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_019ce734-5ba0-7229-84a2-cdaddda20ba7_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:to="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_019d33f9-faa8-77d2-ae5e-63531827098a_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Award Types</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardAwardTypeAndPlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_019ce734-5cd9-7d08-b434-b12787d66031_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_019ce734-5cd9-7bbd-af39-7d7dcdf199a1_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for (Proceeds from) Loans Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromLoansReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:to="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_019ce734-5cd9-778f-9aee-0f3e8f233857_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional claims estimated</link:label>
    <link:label id="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_label_en-US" xlink:label="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Incurred but Not Reported Claims</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:to="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsMember" xlink:to="lab_ecd_EqtyAwrdsAdjsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote</link:label>
    <link:label id="lab_ecd_PnsnBnftsAdjFnTextBlock_label_en-US" xlink:label="lab_ecd_PnsnBnftsAdjFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Benefits Adjustments, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnBnftsAdjFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnBnftsAdjFnTextBlock"/>
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    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_019ce734-5ba0-7b0d-8964-9b612e637368_terseLabel_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments Items [Line Items]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_label_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments [Line Items]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_documentation_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsLineItems" xlink:href="kg-20260331.xsd#kg_RestrictedCashAndInvestmentsLineItems"/>
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    <link:label id="lab_kg_NumberOfDirectors_019ce734-5c52-779c-870f-01602631a1ed_terseLabel_en-US" xlink:label="lab_kg_NumberOfDirectors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of directors</link:label>
    <link:label id="lab_kg_NumberOfDirectors_label_en-US" xlink:label="lab_kg_NumberOfDirectors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Directors</link:label>
    <link:label id="lab_kg_NumberOfDirectors_documentation_en-US" xlink:label="lab_kg_NumberOfDirectors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfDirectors" xlink:href="kg-20260331.xsd#kg_NumberOfDirectors"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfDirectors" xlink:to="lab_kg_NumberOfDirectors" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Amount</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryCompAmt_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryCompAmt" xlink:to="lab_ecd_OutstandingRecoveryCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LukeLedbetterMember_019dcdac-8020-78f3-90f9-e67fc88cbb75_terseLabel_en-US" xlink:label="lab_kg_LukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Luke Ledbetter</link:label>
    <link:label id="lab_kg_LukeLedbetterMember_label_en-US" xlink:label="lab_kg_LukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Luke Ledbetter [Member]</link:label>
    <link:label id="lab_kg_LukeLedbetterMember_documentation_en-US" xlink:label="lab_kg_LukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Luke Ledbetter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LukeLedbetterMember" xlink:href="kg-20260331.xsd#kg_LukeLedbetterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LukeLedbetterMember" xlink:to="lab_kg_LukeLedbetterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SeniorNotes2013Member_019ce734-5cd9-7a07-a86c-2674e3217040_verboseLabel_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes - MHNC &#8211; 7.75%</link:label>
    <link:label id="lab_kg_SeniorNotes2013Member_019ce734-5cd9-7851-b42c-6b1246ecca91_terseLabel_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2013 Senior Notes</link:label>
    <link:label id="lab_kg_SeniorNotes2013Member_label_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes 2013 [Member]</link:label>
    <link:label id="lab_kg_SeniorNotes2013Member_documentation_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes 2013 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2013Member" xlink:href="kg-20260331.xsd#kg_SeniorNotes2013Member"/>
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    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_019ce734-5ba0-75e1-98c2-eae7348c3caf_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentNameDomain_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentNameDomain"/>
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    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_019ce734-5cd9-7624-9c4e-33008a343dc9_verboseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Estimate of Fair Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EstimateOfFairValueFairValueDisclosureMember"/>
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    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_019ce734-5cd9-7bcf-9338-1d69d3d18be4_terseLabel_en-US" xlink:label="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Policy inception, grace period</link:label>
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    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_documentation_en-US" xlink:label="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Contracts, Program Fee Receivables, Premium Receivable, Collection Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:href="kg-20260331.xsd#kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod"/>
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    <link:label id="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember_019d33da-9605-76bd-9ae5-556c7cc2813e_terseLabel_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Market comparable companies &amp; Option Pricing Models</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_019ce734-5c52-764d-b04d-0662c51657e5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsLineItems"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_019ce734-5c52-72e6-8ff2-c5dace2b6f03_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
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    <link:label id="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract_019ce734-5c52-7ca5-955b-f6d6979ae4cc_terseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAccumulatedOtherComprehensiveIncomeCurrentPeriodNetOfTaxAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]</link:label>
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    <link:label id="lab_kg_ReinsuranceAgreementOpen_019ce734-5c52-716d-b0e7-578a989a2b91_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceAgreementOpen" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reinsurance agreements, open</link:label>
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    <link:label id="lab_kg_ReinsuranceAgreementOpen_documentation_en-US" xlink:label="lab_kg_ReinsuranceAgreementOpen" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Open</link:label>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax_019ce734-5c52-77b2-a07e-441a48ab3ce0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossReclassificationAdjustmentFromAOCIForSaleOfSecuritiesBeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Adjustment for reclassification of net realized gains recognized in net loss</link:label>
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    <link:label id="lab_us-gaap_RevenuesAbstract_019ce734-5c52-7580-aee1-e288f3b6e920_terseLabel_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Revenues</link:label>
    <link:label id="lab_us-gaap_RevenuesAbstract_label_en-US" xlink:label="lab_us-gaap_RevenuesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenues [Abstract]</link:label>
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    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_019ce734-5ba0-7397-be08-c0ae2f4eda13_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-U.S. government bonds</link:label>
    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_019ce734-5ba0-7e55-b2be-75b49e62d456_verboseLabel_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Non-U.S. government bonds</link:label>
    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_label_en-US" xlink:label="lab_us-gaap_ForeignGovernmentDebtMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Government Debt [Member]</link:label>
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    <link:label id="lab_kg_RealizedAndUnrealizedLossOnInvestments_019ce734-5cd9-7a5a-8aa5-b1a9f5553319_negatedTotalLabel_en-US" xlink:label="lab_kg_RealizedAndUnrealizedLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized gains (losses) on investment, gross losses</link:label>
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    <link:label id="lab_kg_RealizedAndUnrealizedLossOnInvestments_documentation_en-US" xlink:label="lab_kg_RealizedAndUnrealizedLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Loss On Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealizedAndUnrealizedLossOnInvestments" xlink:href="kg-20260331.xsd#kg_RealizedAndUnrealizedLossOnInvestments"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_019ce734-5c52-72b6-802f-c355c036ea34_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost"/>
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    <link:label id="lab_us-gaap_RestrictedCashAndInvestments_019ce734-5c52-78b2-aa6a-bf12419f5cbb_verboseLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents and investments</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndInvestments_019ce734-5c52-7cac-a7a3-5a077c3c64b8_totalLabel_en-US" xlink:label="lab_us-gaap_RestrictedCashAndInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total restricted cash and investments</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndInvestments_label_en-US" xlink:label="lab_us-gaap_RestrictedCashAndInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_019ce734-5c52-7d40-8840-c93f2f972565_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares - diluted (in shares)</link:label>
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    <link:label id="lab_ecd_NonGaapMeasureDescriptionTextBlock_label_en-US" xlink:label="lab_ecd_NonGaapMeasureDescriptionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-GAAP Measure Description [Text Block]</link:label>
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    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_019ce734-5cd9-7cdc-8de3-c6c72bcf8e23_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Assets from Segment to Consolidated [Table]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation of Assets from Segment to Consolidated [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable"/>
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    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_019ce734-5cd9-731a-a9c6-752381e7eb41_terseLabel_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance</link:label>
    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_019ce734-5cd9-719d-ac5c-e436bd32e2e4_verboseLabel_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance Segment</link:label>
    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_LegacyReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Legacy Reinsurance Segment</link:label>
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    <link:label id="lab_dei_EntitySmallBusiness_019ce734-5c52-7911-8eae-6928ef3be206_terseLabel_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
    <link:label id="lab_dei_EntitySmallBusiness_label_en-US" xlink:label="lab_dei_EntitySmallBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Small Business</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Disclosure [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxDisclosureAbstract"/>
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    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract_019ce734-5cd9-7934-9257-0cb90b7cd3bf_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
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    <link:label id="lab_us-gaap_LossContingencyLossInPeriod_label_en-US" xlink:label="lab_us-gaap_LossContingencyLossInPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Loss in Period</link:label>
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    <link:label id="lab_us-gaap_LongTermDebtTextBlock_019ce734-5c52-7d38-9d6d-b3703d617893_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebtTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList_019ce734-5c52-7a66-82f7-2e64a5f32861_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAssetStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue_019ce734-5c52-7d40-bbcc-625b15cc6bc3_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after one year through five years</link:label>
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    <link:label id="lab_us-gaap_EquityComponentDomain_label_en-US" xlink:label="lab_us-gaap_EquityComponentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Component [Domain]</link:label>
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    <link:label id="lab_kg_AELMember_019ce734-5cd9-7bed-8adc-bf234765f4e7_terseLabel_en-US" xlink:label="lab_kg_AELMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AEL</link:label>
    <link:label id="lab_kg_AELMember_label_en-US" xlink:label="lab_kg_AELMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AEL [Member]</link:label>
    <link:label id="lab_kg_AELMember_documentation_en-US" xlink:label="lab_kg_AELMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AEL [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AELMember" xlink:href="kg-20260331.xsd#kg_AELMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AELMember" xlink:to="lab_kg_AELMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Table</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTableTextBlock"/>
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    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_019ce734-5cd9-76a5-92a8-1184e4b06f93_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Investments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfInvestmentsTable" xlink:type="arc" order="1"/>
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    <link:label id="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare_label_en-US" xlink:label="lab_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Shares Acquired, Average Cost Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockAcquiredAverageCostPerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockAcquiredAverageCostPerShare"/>
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    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_019ce734-5c52-75c6-87ba-b5e5b5aebb3d_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total fair value</link:label>
    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Percent of Total Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Percent of Total Fair Value</link:label>
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    <link:label id="lab_kg_EquityMethodInvestmentsPercentOfTotal_019ce734-5cd9-73a9-8d96-5f11e1e5aefd_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsPercentOfTotal_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Percent Of Total</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsPercentOfTotal_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Percent Of Total</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsPercentOfTotal" xlink:href="kg-20260331.xsd#kg_EquityMethodInvestmentsPercentOfTotal"/>
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    <link:label id="lab_dei_DocumentType_019ce734-5c52-74a9-9da8-585cacb0e4cf_terseLabel_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
    <link:label id="lab_dei_DocumentType_label_en-US" xlink:label="lab_dei_DocumentType" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Type</link:label>
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    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_019ce734-5c52-7293-8015-0f219c22e6db_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Unobservable Inputs (Level 3)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel3Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 3 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel3Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel3Member" xlink:to="lab_us-gaap_FairValueInputsLevel3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock_019ce734-5ba0-77d1-80ed-5406d77b5eaa_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation to Consolidated Total Assets</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation of Assets from Segment to Consolidated [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTextBlock"/>
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    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_019ce734-5c52-7657-bf30-32732cdc9685_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings per Common Share</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareTextBlock_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareTextBlock" xlink:to="lab_us-gaap_EarningsPerShareTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_OutstandingRecoveryIndName_label_en-US" xlink:label="lab_ecd_OutstandingRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Outstanding Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OutstandingRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OutstandingRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OutstandingRecoveryIndName" xlink:to="lab_ecd_OutstandingRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_019ce734-5c52-747d-871c-283aad2cfa31_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent of losses with respect to current lines of business, excluding those above covered business threshold to related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent of Losses With Respect to Current Lines of Business, Excluding Those Above Covered Business Threshold To Related Party</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty"/>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapital_019ce734-5cd9-79e2-ab6d-2268931d868d_terseLabel_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional paid-in capital</link:label>
    <link:label id="lab_us-gaap_AdditionalPaidInCapital_label_en-US" xlink:label="lab_us-gaap_AdditionalPaidInCapital" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional Paid in Capital</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdditionalPaidInCapital" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdditionalPaidInCapital"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AdditionalPaidInCapital" xlink:to="lab_us-gaap_AdditionalPaidInCapital" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProductOrServiceAxis_019ce734-5cd9-77cd-8d1c-e9d5a5925279_terseLabel_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:label id="lab_srt_ProductOrServiceAxis_label_en-US" xlink:label="lab_srt_ProductOrServiceAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductOrServiceAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductOrServiceAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductOrServiceAxis" xlink:to="lab_srt_ProductOrServiceAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements_019ce734-5ba0-7e5c-afbd-00096cb11dd2_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInFundsHeldUnderReinsuranceAgreements"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAcquiredAsPartOfBusinessCombinationTable"/>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_019ce734-5ba0-75dd-8b76-3058eb72783f_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverables on unpaid losses</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables on Unpaid Losses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross"/>
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    <link:label id="lab_us-gaap_CededCreditRiskReinsurerDomain_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskReinsurerDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskReinsurerDomain"/>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_019ce734-5c52-7ed6-9871-c5c33cd69232_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Reserve For Loss And Loss Adjustment Expenses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Reserve For Loss And Loss Adjustment Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReserveForLossAndLossAdjustmentExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssumedPremiumsEarned_019ce734-5c52-7fe4-87e3-5534506e4f0f_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed</link:label>
    <link:label id="lab_us-gaap_AssumedPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_AssumedPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assumed Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssumedPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssumedPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssumedPremiumsEarned" xlink:to="lab_us-gaap_AssumedPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeAxis_019ce734-5ba0-7773-b19c-faa04b1f35c1_terseLabel_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:label id="lab_srt_RangeAxis_label_en-US" xlink:label="lab_srt_RangeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_RangeAxis" xlink:to="lab_srt_RangeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FundsWithheldArrangementMember_019ce734-5c52-72d9-a6d9-d8b54fb0bc53_terseLabel_en-US" xlink:label="lab_kg_FundsWithheldArrangementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income on funds withheld</link:label>
    <link:label id="lab_kg_FundsWithheldArrangementMember_label_en-US" xlink:label="lab_kg_FundsWithheldArrangementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Funds Withheld Arrangement [Member]</link:label>
    <link:label id="lab_kg_FundsWithheldArrangementMember_documentation_en-US" xlink:label="lab_kg_FundsWithheldArrangementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Funds Withheld Arrangement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FundsWithheldArrangementMember" xlink:href="kg-20260331.xsd#kg_FundsWithheldArrangementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FundsWithheldArrangementMember" xlink:to="lab_kg_FundsWithheldArrangementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivateCreditLendingMember_019ce734-5ba0-777a-b2c6-553507c6b327_verboseLabel_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Private credit investments</link:label>
    <link:label id="lab_kg_PrivateCreditLendingMember_label_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Credit Lending [Member]</link:label>
    <link:label id="lab_kg_PrivateCreditLendingMember_documentation_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Private Credit Lending</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivateCreditLendingMember" xlink:href="kg-20260331.xsd#kg_PrivateCreditLendingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivateCreditLendingMember" xlink:to="lab_kg_PrivateCreditLendingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_019ce734-5ba0-7359-b4ba-0ab5915c57c7_terseLabel_en-US" xlink:label="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premium Repayment Loan Agreement</link:label>
    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_label_en-US" xlink:label="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premium Repayment Loan Agreement [Member]</link:label>
    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_documentation_en-US" xlink:label="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premium Repayment Loan Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumRepaymentLoanAgreementMember" xlink:href="kg-20260331.xsd#kg_PremiumRepaymentLoanAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PremiumRepaymentLoanAgreementMember" xlink:to="lab_kg_PremiumRepaymentLoanAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MarketableSecuritiesRealizedGain_019ce734-5cd9-7369-a7a4-c6c7a221079b_terseLabel_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedGain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments, gross gains</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedGain_label_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedGain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Gain</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedGain_documentation_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedGain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MarketableSecuritiesRealizedGain" xlink:href="kg-20260331.xsd#kg_MarketableSecuritiesRealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MarketableSecuritiesRealizedGain" xlink:to="lab_kg_MarketableSecuritiesRealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompAmt_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:label id="lab_ecd_AggtErrCompAmt_label_en-US" xlink:label="lab_ecd_AggtErrCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtErrCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtErrCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompAmt" xlink:to="lab_ecd_AggtErrCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_019ce734-5cd9-7627-82db-6b1714f51c61_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maximum limit of liability attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Maximum Limit of Liability Attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Maximum Limit of Liability Attaching</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:to="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote</link:label>
    <link:label id="lab_ecd_PeerGroupIssuersFnTextBlock_label_en-US" xlink:label="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Peer Group Issuers, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeerGroupIssuersFnTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeerGroupIssuersFnTextBlock" xlink:to="lab_ecd_PeerGroupIssuersFnTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_019ce734-5c52-7c67-a88b-8684fe7d8e72_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss attributable to Kestrel common shareholders, basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_019ce734-5ba0-7ffe-be17-3aff5e7eb12a_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramDomain_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ShareRepurchaseProgramDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ShareRepurchaseProgramDomain" xlink:to="lab_srt_ShareRepurchaseProgramDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnershipAtMergerClosingMember_019ce734-5ba1-73f1-bd78-33b06d0cd2d7_terseLabel_en-US" xlink:label="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Ownership, Issued at closing of Combination</link:label>
    <link:label id="lab_kg_InvestmentOwnershipAtMergerClosingMember_label_en-US" xlink:label="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Ownership, At Merger Closing [Member]</link:label>
    <link:label id="lab_kg_InvestmentOwnershipAtMergerClosingMember_documentation_en-US" xlink:label="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Ownership, At Merger Closing</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnershipAtMergerClosingMember" xlink:href="kg-20260331.xsd#kg_InvestmentOwnershipAtMergerClosingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentOwnershipAtMergerClosingMember" xlink:to="lab_kg_InvestmentOwnershipAtMergerClosingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019ce734-5c52-7a95-9033-130c79d3704d_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss, after tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_019ce734-5c52-717f-b248-ab1d08652c97_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net current period other comprehensive (loss) income</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Net of Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_019ce734-5ba0-70c9-9355-608578a09355_terseLabel_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Thereafter</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_label_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Payments Due After Year Four</link:label>
    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour_documentation_en-US" xlink:label="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, Payments Due After Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:href="kg-20260331.xsd#kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:to="lab_kg_LesseeOperatingLeaseLiabilityPaymentsDueAfterYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingExpenses_019ce734-5cd9-7207-af82-14ca71d3a122_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_OperatingExpenses_label_en-US" xlink:label="lab_us-gaap_OperatingExpenses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Expenses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingExpenses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingExpenses"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingExpenses" xlink:to="lab_us-gaap_OperatingExpenses" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019ce734-5cd9-708d-8de1-44673c6f9d7f_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group Ltd share price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_019ce734-5cd9-71f5-a078-e57891cfd18e_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group Ltd share price (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionSharePrice_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Price Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionSharePrice"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionSharePrice" xlink:to="lab_us-gaap_BusinessAcquisitionSharePrice" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceAgreementCompletingRunOff_019ce734-5c52-7eb2-95c5-3dc6332bbfef_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of reinsurance agreements, completing run-off</link:label>
    <link:label id="lab_kg_ReinsuranceAgreementCompletingRunOff_label_en-US" xlink:label="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Completing Run-Off</link:label>
    <link:label id="lab_kg_ReinsuranceAgreementCompletingRunOff_documentation_en-US" xlink:label="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Completing Run-Off</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAgreementCompletingRunOff" xlink:href="kg-20260331.xsd#kg_ReinsuranceAgreementCompletingRunOff"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceAgreementCompletingRunOff" xlink:to="lab_kg_ReinsuranceAgreementCompletingRunOff" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_019ce734-5cd9-7667-8a28-2eb2cc990925_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Quoted Prices in Active Markets for Identical Assets (Level 1)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel1Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel1Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel1Member" xlink:to="lab_us-gaap_FairValueInputsLevel1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StandardPoorsAAARatingMember_019ce734-5c52-79a9-b428-0509d2c83ba3_terseLabel_en-US" xlink:label="lab_srt_StandardPoorsAAARatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AAA</link:label>
    <link:label id="lab_srt_StandardPoorsAAARatingMember_label_en-US" xlink:label="lab_srt_StandardPoorsAAARatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, AAA Rating [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StandardPoorsAAARatingMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StandardPoorsAAARatingMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StandardPoorsAAARatingMember" xlink:to="lab_srt_StandardPoorsAAARatingMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_019ce734-5cd9-7df0-983d-d273c37906e3_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Related Party Transactions, by Related Party [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:to="lab_us-gaap_ScheduleOfRelatedPartyTransactionsByRelatedPartyTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_019ce734-5ba0-7569-83b3-02adac8cd57c_totalLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Diluted loss per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareDiluted_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareDiluted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Diluted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareDiluted" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareDiluted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareDiluted" xlink:to="lab_us-gaap_EarningsPerShareDiluted" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVenture3Member_019ce734-5c52-7079-bde4-c2b12083ed4c_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVenture3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Venture 3</link:label>
    <link:label id="lab_kg_SilverstoneVenture3Member_label_en-US" xlink:label="lab_kg_SilverstoneVenture3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture 3 [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVenture3Member_documentation_en-US" xlink:label="lab_kg_SilverstoneVenture3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVenture3Member" xlink:href="kg-20260331.xsd#kg_SilverstoneVenture3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVenture3Member" xlink:to="lab_kg_SilverstoneVenture3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_019ce734-5c52-7eea-a762-acd25f987661_totalLabel_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains, net of deferred income tax</link:label>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_label_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Gross Unrealized Gain (Loss), Net of Deferred Income Tax Expense</link:label>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_documentation_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Gross Unrealized Gain (Loss), Net of Deferred Income Tax Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:href="kg-20260331.xsd#kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:to="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_019ce734-5c52-77e1-89ea-e57b6735a294_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due after five years through ten years</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, after Year 5 Through 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTableLineItems_019ce734-5c52-7250-9876-0a11c610b3c6_terseLabel_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities Table [Line Items]</link:label>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTableLineItems_label_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fixed Maturities Table [Line Items]</link:label>
    <link:label id="lab_kg_ScheduleofFixedMaturitiesTableLineItems_documentation_en-US" xlink:label="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">[Line Items] for Schedule of Fixed Maturities Table [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:href="kg-20260331.xsd#kg_ScheduleofFixedMaturitiesTableLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:to="lab_kg_ScheduleofFixedMaturitiesTableLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019ce734-5c52-7e3a-8508-6dc2b74d65c2_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares, at cost (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_019ce734-5c52-72f1-ade2-201cd6eba0e0_netLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Treasury shares (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonShares" xlink:to="lab_us-gaap_TreasuryStockCommonShares" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsMember_019ce734-5cd9-7ea6-a688-230b0cb321db_terseLabel_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings</link:label>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsMember_label_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings [Member]</link:label>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsMember_documentation_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:href="kg-20260331.xsd#kg_KestrelIntermediateLedbetterHoldingsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:to="lab_kg_KestrelIntermediateLedbetterHoldingsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidationItemsDomain_019ce734-5c52-773d-ae05-a01e304f3cb9_terseLabel_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:label id="lab_srt_ConsolidationItemsDomain_label_en-US" xlink:label="lab_srt_ConsolidationItemsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation Items [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidationItemsDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidationItemsDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidationItemsDomain" xlink:to="lab_srt_ConsolidationItemsDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration_019d3d06-b6b1-7795-baaf-e1c1075c1fd7_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Derivative Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration" xlink:to="lab_us-gaap_DerivativeLiabilityStatementOfFinancialPositionExtensibleEnumeration" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipDomain_019df410-7564-77f0-82d6-2241971b778e_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Domain]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipDomain_label_en-US" xlink:label="lab_kg_CommonStockOwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Domain]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipDomain_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipDomain" xlink:href="kg-20260331.xsd#kg_CommonStockOwnershipDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockOwnershipDomain" xlink:to="lab_kg_CommonStockOwnershipDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_019d33da-9605-7a3e-8119-c6fc4f3744c9_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Value Change - Market/Industry Factors</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_label_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company TIC [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Change in Guideline Public Company TIC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:href="kg-20260331.xsd#kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:to="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_019ce734-5c52-7cfc-b914-15afac9bfe81_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
    <link:label id="lab_us-gaap_CededCreditRiskAxis_label_en-US" xlink:label="lab_us-gaap_CededCreditRiskAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededCreditRiskAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededCreditRiskAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededCreditRiskAxis" xlink:to="lab_us-gaap_CededCreditRiskAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019ce734-5c52-7e93-b765-d266383aee41_periodStartLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Less: reinsurance recoverable on unpaid losses, January 1</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_019ce734-5c52-727b-8005-9f66c8b8580e_periodEndLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses, March 31</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables, Including Reinsurance Premium Paid</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverables" xlink:to="lab_us-gaap_ReinsuranceRecoverables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_019ce734-5cd9-7d3c-95b6-25499365fb7e_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:to="lab_us-gaap_ScheduleOfGainLossOnInvestmentsIncludingMarketableSecuritiesAndInvestmentsHeldAtCostIncomeStatementReportedAmountsSummaryLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_HistoricReinsuranceMember_019ce734-5c52-72fc-8b24-d54383720ddc_terseLabel_en-US" xlink:label="lab_kg_HistoricReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Historic Reinsurance</link:label>
    <link:label id="lab_kg_HistoricReinsuranceMember_label_en-US" xlink:label="lab_kg_HistoricReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Historic Reinsurance [Member]</link:label>
    <link:label id="lab_kg_HistoricReinsuranceMember_documentation_en-US" xlink:label="lab_kg_HistoricReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Historic Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_HistoricReinsuranceMember" xlink:href="kg-20260331.xsd#kg_HistoricReinsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_HistoricReinsuranceMember" xlink:to="lab_kg_HistoricReinsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupCommonStockMember_019ddfc5-b3ad-7016-ad34-25157cdd5b37_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group, Common Stock</link:label>
    <link:label id="lab_kg_KestrelGroupCommonStockMember_label_en-US" xlink:label="lab_kg_KestrelGroupCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Group, Common Stock [Member]</link:label>
    <link:label id="lab_kg_KestrelGroupCommonStockMember_documentation_en-US" xlink:label="lab_kg_KestrelGroupCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Group, Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupCommonStockMember" xlink:href="kg-20260331.xsd#kg_KestrelGroupCommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupCommonStockMember" xlink:to="lab_kg_KestrelGroupCommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_019ce734-5c52-7462-99e7-475c6c527bc1_terseLabel_en-US" xlink:label="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of outstanding debt holders in lawsuit (at least)</link:label>
    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_label_en-US" xlink:label="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingency, Percentage of Outstanding Debt Holders Involved in Lawsuit</link:label>
    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_documentation_en-US" xlink:label="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loss Contingency, Percentage of Outstanding Debt Holders Involved in Lawsuit</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:href="kg-20260331.xsd#kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:to="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_019ce734-5c52-7257-96b3-2c43a45f7ddf_terseLabel_en-US" xlink:label="lab_us-gaap_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Corporate bonds</link:label>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_CorporateBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Corporate Bond Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateBondSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateBondSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateBondSecuritiesMember" xlink:to="lab_us-gaap_CorporateBondSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_019d3d3a-b9f3-79b0-9ba5-3c0d4c5a14e0_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2028</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_019ce734-5ba0-77c7-98c4-dfb82ee70c4f_terseLabel_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Axis]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_label_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Axis]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_documentation_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeAxis" xlink:href="kg-20260331.xsd#kg_InvestmentMilestoneTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentMilestoneTypeAxis" xlink:to="lab_kg_InvestmentMilestoneTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementNo.1Member_019ce734-5c52-769e-813a-bcc7917660d3_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 1</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.1Member_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.1Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 1 [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.1Member_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.1Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 1 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementNo.1Member" xlink:href="kg-20260331.xsd#kg_PostTerminationEndorsementNo.1Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementNo.1Member" xlink:to="lab_kg_PostTerminationEndorsementNo.1Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019ce734-5c52-7cb4-8ac3-5f2c5c42c82f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior notes - principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_019ce734-5c52-7274-9b15-99777b025774_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCarryingAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCarryingAmount" xlink:to="lab_us-gaap_DebtInstrumentCarryingAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementMember_019ce734-5cd9-70de-8855-93b03b8ac770_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMember_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMember_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMember" xlink:href="kg-20260331.xsd#kg_PostTerminationEndorsementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementMember" xlink:to="lab_kg_PostTerminationEndorsementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_019ce734-5cd9-7bea-a06c-a5b2762da63c_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock owned by shareholder (in shares)</link:label>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_label_en-US" xlink:label="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Owned, Balance, Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentOwnedBalanceShares" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentOwnedBalanceShares"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentOwnedBalanceShares" xlink:to="lab_us-gaap_InvestmentOwnedBalanceShares" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrExpirationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration Date</link:label>
    <link:label id="lab_ecd_TrdArrExpirationDate_label_en-US" xlink:label="lab_ecd_TrdArrExpirationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Expiration Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrExpirationDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrExpirationDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrExpirationDate" xlink:to="lab_ecd_TrdArrExpirationDate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_019ce734-5c52-7840-b50c-19d6ce40e150_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction amount (returned)</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Amounts of Transaction</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAmountsOfTransaction"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:to="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_019ce734-5ba0-7f35-b36a-b2a6626aeeed_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EQUITY</link:label>
    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_label_en-US" xlink:label="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity, Including Portion Attributable to Noncontrolling Interest [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:to="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted_019ce734-5c52-7474-96e8-9a403362aaa5_terseLabel_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative arrangement, reserves expected to be commuted</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted_label_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted_documentation_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:href="kg-20260331.xsd#kg_CollaborativeArrangementReservesExpectedToBeCommuted"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:to="lab_kg_CollaborativeArrangementReservesExpectedToBeCommuted" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_019ce734-5cd9-772f-a6c3-b9f1305f6f5d_terseLabel_en-US" xlink:label="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities</link:label>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Income Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedIncomeSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedIncomeSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedIncomeSecuritiesMember" xlink:to="lab_us-gaap_FixedIncomeSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInvestmentsMember_019ce734-5c52-7f7a-ad29-d6f38f02a5e6_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other equity method investments at fair value option elected</link:label>
    <link:label id="lab_us-gaap_OtherInvestmentsMember_019d33da-9605-7de9-bbff-5a50ddfb84c0_netLabel_en-US" xlink:label="lab_us-gaap_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestmentsMember_019ce734-5c52-72b0-9647-d1a072b9d677_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total unfunded commitments on other investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_OtherInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestmentsMember" xlink:to="lab_us-gaap_OtherInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_019ce734-5ba1-74a9-877f-22c36c413253_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments and Carrying Value and Beneficial Ownership Percentage of Equity Method Investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsTextBlock" xlink:to="lab_us-gaap_EquityMethodInvestmentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededPremiumsWritten_019ce734-5c52-757e-80c0-8ac4d0fb04be_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CededPremiumsWritten" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Ceded</link:label>
    <link:label id="lab_us-gaap_CededPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_CededPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededPremiumsWritten" xlink:to="lab_us-gaap_CededPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_terseLabel_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income</link:label>
    <link:label id="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock_label_en-US" xlink:label="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Compensation Actually Paid vs. Net Income [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CompActuallyPaidVsNetIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:to="lab_ecd_CompActuallyPaidVsNetIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_019ce734-5c52-7425-8795-9a94617291bf_terseLabel_en-US" xlink:label="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">A+, A, A-</link:label>
    <link:label id="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_label_en-US" xlink:label="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's SingleA Plus, SingleA, and SingleA Minus [Member]</link:label>
    <link:label id="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_documentation_en-US" xlink:label="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, A-Plus, A, A- Rating [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:href="kg-20260331.xsd#kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:to="lab_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCurrentReportingStatus_019ce734-5c52-7cff-914d-58c69c80b5ea_terseLabel_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:label id="lab_dei_EntityCurrentReportingStatus_label_en-US" xlink:label="lab_dei_EntityCurrentReportingStatus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Current Reporting Status</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCurrentReportingStatus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCurrentReportingStatus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCurrentReportingStatus" xlink:to="lab_dei_EntityCurrentReportingStatus" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscTable_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscTable" xlink:to="lab_ecd_AwardsCloseToMnpiDiscTable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_019ce734-5c52-7ce0-965d-52f4630c21b7_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesDomain_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesDomain" xlink:to="lab_srt_ConsolidatedEntitiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_019ce734-5c52-7146-aa65-1e0ee5dd2ace_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearAmortizedCost"/>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross_019ce734-5cd9-7e2e-a34d-9b447fdbed73_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverables on paid losses, gross</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverables on Paid Losses, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesOnPaidLossesGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:to="lab_us-gaap_ReinsuranceRecoverablesOnPaidLossesGross" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfIndependentDirectors_019ce734-5cd9-759b-abe8-a24ec55649d1_terseLabel_en-US" xlink:label="lab_kg_NumberOfIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of independent directors</link:label>
    <link:label id="lab_kg_NumberOfIndependentDirectors_label_en-US" xlink:label="lab_kg_NumberOfIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Independent Directors</link:label>
    <link:label id="lab_kg_NumberOfIndependentDirectors_documentation_en-US" xlink:label="lab_kg_NumberOfIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Independent Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfIndependentDirectors" xlink:href="kg-20260331.xsd#kg_NumberOfIndependentDirectors"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfIndependentDirectors" xlink:to="lab_kg_NumberOfIndependentDirectors" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019ce734-5ba0-7a44-b95c-0cf1a95a2ab5_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_019ce734-5ba0-7f46-b9e9-ab6079cb89ce_verboseLabel_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_FinancialInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_FinancialInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialInstrumentAxis" xlink:to="lab_us-gaap_FinancialInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BenefitsLossesAndExpensesAbstract_019ce734-5cd9-7715-85bb-7585fbbdda44_terseLabel_en-US" xlink:label="lab_us-gaap_BenefitsLossesAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expenses</link:label>
    <link:label id="lab_us-gaap_BenefitsLossesAndExpensesAbstract_label_en-US" xlink:label="lab_us-gaap_BenefitsLossesAndExpensesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BenefitsLossesAndExpensesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BenefitsLossesAndExpensesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BenefitsLossesAndExpensesAbstract" xlink:to="lab_us-gaap_BenefitsLossesAndExpensesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_019ce734-5cd9-7f71-b92c-15c88ab0f769_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfFinancialPositionAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Financial Position [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfFinancialPositionAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfFinancialPositionAbstract" xlink:to="lab_us-gaap_StatementOfFinancialPositionAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_terseLabel_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Executive Category:</link:label>
    <link:label id="lab_ecd_ExecutiveCategoryAxis_label_en-US" xlink:label="lab_ecd_ExecutiveCategoryAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Executive Category [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ExecutiveCategoryAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ExecutiveCategoryAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ExecutiveCategoryAxis" xlink:to="lab_ecd_ExecutiveCategoryAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GeorgeKarfunkelMember_019ce734-5ba0-7c5d-a4dc-938704e56d06_terseLabel_en-US" xlink:label="lab_kg_GeorgeKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">George Karfunkel</link:label>
    <link:label id="lab_kg_GeorgeKarfunkelMember_label_en-US" xlink:label="lab_kg_GeorgeKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">George Karfunkel [Member]</link:label>
    <link:label id="lab_kg_GeorgeKarfunkelMember_documentation_en-US" xlink:label="lab_kg_GeorgeKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">George Karfunkel [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GeorgeKarfunkelMember" xlink:href="kg-20260331.xsd#kg_GeorgeKarfunkelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GeorgeKarfunkelMember" xlink:to="lab_kg_GeorgeKarfunkelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_019ce734-5cd9-75ca-a2ec-c57cac735796_terseLabel_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Data</link:label>
    <link:label id="lab_dei_CurrentFiscalYearEndDate_label_en-US" xlink:label="lab_dei_CurrentFiscalYearEndDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Fiscal Year End Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CurrentFiscalYearEndDate" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CurrentFiscalYearEndDate"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_019ce734-5c52-7ef0-948b-72a86b2a1ddf_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Major Class Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain"/>
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    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1_019ce734-5c52-76b8-80c4-098f32aaaa30_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net paid losses related to Prior years</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Claims Paid, Prior Years</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidPriorYears1"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_019ce734-5ba1-7fdb-a37b-89166b3cf705_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares remain for future issuance (in shares)</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant"/>
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    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_019d33d0-ebec-7f00-b0b6-a9d70cd92b9a_terseLabel_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets, fair value disclosure, number of securities priced for fair value</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_label_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Number Of Securities Priced For Fair Value</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_documentation_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Number Of Securities Priced For Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:href="kg-20260331.xsd#kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue"/>
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    <link:label id="lab_us-gaap_DerivativeLiabilities_019ce734-5c52-73c8-a3cd-bbabf57bed50_terseLabel_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underwriting-related derivative liability</link:label>
    <link:label id="lab_us-gaap_DerivativeLiabilities_label_en-US" xlink:label="lab_us-gaap_DerivativeLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Derivative Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DerivativeLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DerivativeLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DerivativeLiabilities" xlink:to="lab_us-gaap_DerivativeLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag_019ce734-5c52-7356-99a7-06ae94151191_terseLabel_en-US" xlink:label="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value recurring basis unobservable input reconciliation asset gain loss statement of other comprehensive income extensible list not disclosed flag</link:label>
    <link:label id="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag_label_en-US" xlink:label="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Asset Gain Loss Statement Of Other Comprehensive Income Extensible List Not Disclosed Flag</link:label>
    <link:label id="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag_documentation_en-US" xlink:label="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Recurring Basis Unobservable Input Reconciliation Asset Gain Loss Statement Of Other Comprehensive Income Extensible List Not Disclosed Flag</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:href="kg-20260331.xsd#kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:to="lab_kg_FairValueRecurringBasisUnobservableInputReconciliationAssetGainLossStatementOfOtherComprehensiveIncomeExtensibleListNotDisclosedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_terseLabel_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in Compensation Table</link:label>
    <link:label id="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember_label_en-US" xlink:label="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Awards Adjustments, Excluding Value Reported in the Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:to="lab_ecd_EqtyAwrdsAdjsExclgValRprtdInSummryCompstnTblMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessAcquisitionCostsMember_019ddf81-bc35-7bc8-85c9-535adb42a069_terseLabel_en-US" xlink:label="lab_kg_BusinessAcquisitionCostsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission and Other Acquisition Expenses</link:label>
    <link:label id="lab_kg_BusinessAcquisitionCostsMember_label_en-US" xlink:label="lab_kg_BusinessAcquisitionCostsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition Costs [Member]</link:label>
    <link:label id="lab_kg_BusinessAcquisitionCostsMember_documentation_en-US" xlink:label="lab_kg_BusinessAcquisitionCostsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisition Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessAcquisitionCostsMember" xlink:href="kg-20260331.xsd#kg_BusinessAcquisitionCostsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessAcquisitionCostsMember" xlink:to="lab_kg_BusinessAcquisitionCostsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_019ce734-5c52-73eb-bc3a-ce0874ffa958_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Liabilities held for sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Liabilities Held For Sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Liabilities Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_019ce734-5ba0-7ca9-a507-4aea43d983bc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Measured at Fair Value on a Recurring Basis</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value, Assets and Liabilities Measured on Recurring Basis [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_019ce734-5c52-79d9-bfd1-78c07fbb87d3_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity securities: at fair value (Cost: 2026: $11,145; 2025: $11,145)</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_019ce734-5c52-7af3-a7b4-33f18d37080f_netLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Fair Value</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_019ce734-5c52-7c6f-bd79-b989b3058f14_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNi" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNi" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNi"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNi" xlink:to="lab_us-gaap_EquitySecuritiesFvNi" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnership5PercentMember_019ce734-5cd9-71ef-a016-0dc5e6bb981a_terseLabel_en-US" xlink:label="lab_kg_InvestmentOwnership5PercentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Ownership, 5%</link:label>
    <link:label id="lab_kg_InvestmentOwnership5PercentMember_label_en-US" xlink:label="lab_kg_InvestmentOwnership5PercentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Ownership, 5 Percent [Member]</link:label>
    <link:label id="lab_kg_InvestmentOwnership5PercentMember_documentation_en-US" xlink:label="lab_kg_InvestmentOwnership5PercentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Ownership, 5 Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnership5PercentMember" xlink:href="kg-20260331.xsd#kg_InvestmentOwnership5PercentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentOwnership5PercentMember" xlink:to="lab_kg_InvestmentOwnership5PercentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_019ce734-5c52-74fd-9a7d-32bb757a6bbb_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_019ce734-5c52-79c9-bf13-eeaef3f6ccdd_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired to Liability Assumed, Excess (Less)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_019ce734-5cd9-7999-82c5-4954b4f221d1_terseLabel_en-US" xlink:label="lab_kg_InvestmentOwnership25PercentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Ownership, 25%</link:label>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_label_en-US" xlink:label="lab_kg_InvestmentOwnership25PercentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Ownership, 25 Percent [Member]</link:label>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_documentation_en-US" xlink:label="lab_kg_InvestmentOwnership25PercentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Ownership, 25 Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentOwnership25PercentMember" xlink:href="kg-20260331.xsd#kg_InvestmentOwnership25PercentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentOwnership25PercentMember" xlink:to="lab_kg_InvestmentOwnership25PercentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealEstateInvestmentsAtFairValueMember_019ce734-5ba1-7110-b587-b29a9897f823_terseLabel_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investments at fair value option elected</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtFairValueMember_label_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Fair Value [Member]</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtFairValueMember_documentation_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealEstateInvestmentsAtFairValueMember" xlink:href="kg-20260331.xsd#kg_RealEstateInvestmentsAtFairValueMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RealEstateInvestmentsAtFairValueMember" xlink:to="lab_kg_RealEstateInvestmentsAtFairValueMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_019ce734-5c52-7306-93f8-2091fa420105_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in financing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureAxis_terseLabel_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measure:</link:label>
    <link:label id="lab_ecd_MeasureAxis_label_en-US" xlink:label="lab_ecd_MeasureAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureAxis" xlink:to="lab_ecd_MeasureAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_019ce734-5ba0-7db4-b935-348f5ad71d3c_terseLabel_en-US" xlink:label="lab_kg_MaidenHoldingsLtd.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maiden Holdings, Ltd.</link:label>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_label_en-US" xlink:label="lab_kg_MaidenHoldingsLtd.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maiden Holdings, Ltd. [Member]</link:label>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_documentation_en-US" xlink:label="lab_kg_MaidenHoldingsLtd.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maiden Holdings, Ltd. [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenHoldingsLtd.Member" xlink:href="kg-20260331.xsd#kg_MaidenHoldingsLtd.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MaidenHoldingsLtd.Member" xlink:to="lab_kg_MaidenHoldingsLtd.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_019ce734-5cd9-7207-a45d-364e05740028_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueAxis_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueAxis" xlink:to="lab_us-gaap_ValuationTechniqueAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SeidenLPSeidenMGMTLPMember_019ce734-5cd9-768e-a7dc-e8326fd443dd_terseLabel_en-US" xlink:label="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Seiden LP &amp; Seiden MGMT LP</link:label>
    <link:label id="lab_kg_SeidenLPSeidenMGMTLPMember_label_en-US" xlink:label="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Seiden LP &amp; Seiden MGMT LP [Member]</link:label>
    <link:label id="lab_kg_SeidenLPSeidenMGMTLPMember_documentation_en-US" xlink:label="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Seiden LP &amp; Seiden MGMT LP</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeidenLPSeidenMGMTLPMember" xlink:href="kg-20260331.xsd#kg_SeidenLPSeidenMGMTLPMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SeidenLPSeidenMGMTLPMember" xlink:to="lab_kg_SeidenLPSeidenMGMTLPMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_019ce734-5c52-7cd2-8a10-cc04f3e63bd1_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationDomain_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationDomain" xlink:to="lab_us-gaap_DisposalGroupClassificationDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BenefitsLossesAndExpensesNet_019ce734-5c52-75f0-a552-4f0b23108d84_totalLabel_en-US" xlink:label="lab_kg_BenefitsLossesAndExpensesNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total expenses</link:label>
    <link:label id="lab_kg_BenefitsLossesAndExpensesNet_label_en-US" xlink:label="lab_kg_BenefitsLossesAndExpensesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses, Net</link:label>
    <link:label id="lab_kg_BenefitsLossesAndExpensesNet_documentation_en-US" xlink:label="lab_kg_BenefitsLossesAndExpensesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Benefits, Losses and Expenses, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BenefitsLossesAndExpensesNet" xlink:href="kg-20260331.xsd#kg_BenefitsLossesAndExpensesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BenefitsLossesAndExpensesNet" xlink:to="lab_kg_BenefitsLossesAndExpensesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTableTextBlock_terseLabel_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure, Table</link:label>
    <link:label id="lab_ecd_PvpTableTextBlock_label_en-US" xlink:label="lab_ecd_PvpTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTableTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTableTextBlock" xlink:to="lab_ecd_PvpTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Violation of Home Country Law, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToViolationOfHomeCountryLawAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_019ce734-5c52-758a-b70d-88a232ef4614_terseLabel_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization for the fair value adjustment</link:label>
    <link:label id="lab_us-gaap_AmortizationOfFinancingCosts_label_en-US" xlink:label="lab_us-gaap_AmortizationOfFinancingCosts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amortization of Debt Issuance Costs</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AmortizationOfFinancingCosts" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AmortizationOfFinancingCosts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AmortizationOfFinancingCosts" xlink:to="lab_us-gaap_AmortizationOfFinancingCosts" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_019ce734-5cd9-7944-a3da-7e7f6241c4c0_terseLabel_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses of unrealized loss positions</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_label_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Continuous Unrealized Loss Position, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="kg-20260331.xsd#kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:to="lab_kg_InvestmentsContinuousUnrealizedLossPositionAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_019ce734-5c52-7115-963f-f0ec485f0df2_negatedLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Investment expenses</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInvestmentExpense_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Investment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInvestmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInvestmentExpense" xlink:to="lab_us-gaap_InvestmentIncomeInvestmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_019ce734-5c52-7a45-b8ba-9816820fedaf_terseLabel_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:label id="lab_dei_EntityTaxIdentificationNumber_label_en-US" xlink:label="lab_dei_EntityTaxIdentificationNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Tax Identification Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityTaxIdentificationNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityTaxIdentificationNumber"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityTaxIdentificationNumber" xlink:to="lab_dei_EntityTaxIdentificationNumber" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_019ce734-5cd9-71a8-92c0-df057c76e7ac_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flows</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDiscountedCashFlowMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:to="lab_us-gaap_ValuationTechniqueDiscountedCashFlowMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_019ce734-5c52-717f-8c26-424c8567e10e_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value of securities without single maturities</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, without Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_019ce734-5c52-7dcc-b892-9fed495d56e7_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Domain]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Domain]</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, By Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeDomain" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionByTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionByTypeDomain" xlink:to="lab_kg_RelatedPartyTransactionByTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_019ce734-5c52-7f67-8eef-ff2ba50e29c1_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, issued (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesIssued_label_en-US" xlink:label="lab_us-gaap_CommonStockSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Shares, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockSharesIssued"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockSharesIssued" xlink:to="lab_us-gaap_CommonStockSharesIssued" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_019ce734-5c52-7ad0-9142-9d92c3632664_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average remaining lease term</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Weighted Average Remaining Lease Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:to="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_019ce734-5c52-7b45-8990-54e277d822cb_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable for paid and unpaid claims and claims adjustments, adverse development cover</link:label>
    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_label_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable For Paid And Unpaid Claims And Claims Adjustments, Adverse Development Cover</link:label>
    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_documentation_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable For Paid And Unpaid Claims And Claims Adjustments, Adverse Development Cover</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:href="kg-20260331.xsd#kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover"/>
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    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_019ce734-5c52-7825-9867-956fe1240de5_terseLabel_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. agency bonds&#160;&#8211;&#160;mortgage-backed</link:label>
    <link:label id="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_label_en-US" xlink:label="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Mortgage-Backed Security, Issued by US Government-Sponsored Enterprise [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember"/>
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    <link:label id="lab_ecd_TradingArrAxis_terseLabel_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangement:</link:label>
    <link:label id="lab_ecd_TradingArrAxis_label_en-US" xlink:label="lab_ecd_TradingArrAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TradingArrAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TradingArrAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TradingArrAxis" xlink:to="lab_ecd_TradingArrAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_019ce734-5cd9-7c34-8bbe-d35c4a49caf7_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrealized losses</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Accumulated Loss [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_terseLabel_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:label id="lab_ecd_TotalShareholderRtnAmt_label_en-US" xlink:label="lab_ecd_TotalShareholderRtnAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Total Shareholder Return Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TotalShareholderRtnAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TotalShareholderRtnAmt"/>
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    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_019ce734-5c52-7118-8869-3aa21ddcc6c7_terseLabel_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Domain]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_label_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Domain]</link:label>
    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_documentation_en-US" xlink:label="lab_kg_InvestmentMilestoneTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Milestone, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentMilestoneTypeDomain" xlink:href="kg-20260331.xsd#kg_InvestmentMilestoneTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentMilestoneTypeDomain" xlink:to="lab_kg_InvestmentMilestoneTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_019ce734-5cd9-7fcc-9310-2cc7255651c0_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 2</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 2 [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementNo.2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement No. 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementNo.2Member" xlink:href="kg-20260331.xsd#kg_PostTerminationEndorsementNo.2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementNo.2Member" xlink:to="lab_kg_PostTerminationEndorsementNo.2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_019ce734-5c52-7027-b2d8-92ebf26c4c7e_verboseLabel_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Corporate assets</link:label>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_label_en-US" xlink:label="lab_us-gaap_CorporateNonSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Reconciling Item, Corporate Nonsegment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CorporateNonSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CorporateNonSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CorporateNonSegmentMember" xlink:to="lab_us-gaap_CorporateNonSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_SecurityExchangeName_019ce734-5c52-79c5-bce4-f2f0a5146f54_terseLabel_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:label id="lab_dei_SecurityExchangeName_label_en-US" xlink:label="lab_dei_SecurityExchangeName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Security Exchange Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_SecurityExchangeName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_SecurityExchangeName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_SecurityExchangeName" xlink:to="lab_dei_SecurityExchangeName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019ce734-5ba0-7f3e-b652-abc765f8788b_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable, allowance for credit loss</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019ce734-5ba0-71a0-b640-1cce36026b9a_periodStartLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses on reinsurance recoverable, beginning of period</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_019ce734-5ba0-7be4-b42c-c352ad64bc5b_periodEndLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses on reinsurance recoverable, end of period</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverablesAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverablesAllowance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverablesAllowance" xlink:to="lab_us-gaap_ReinsuranceRecoverablesAllowance" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeAxis_019ce734-5c52-79a2-9989-0d54310af5b4_terseLabel_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Axis]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeAxis_label_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Axis]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeAxis_documentation_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:href="kg-20260331.xsd#kg_RestrictedCashAndInvestmentsTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:to="lab_kg_RestrictedCashAndInvestmentsTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CededPremiumsEarned_019ce734-5ba0-7590-baf5-37371c046107_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_CededPremiumsEarned" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Ceded</link:label>
    <link:label id="lab_us-gaap_CededPremiumsEarned_label_en-US" xlink:label="lab_us-gaap_CededPremiumsEarned" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ceded Premiums Earned</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CededPremiumsEarned" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CededPremiumsEarned"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CededPremiumsEarned" xlink:to="lab_us-gaap_CededPremiumsEarned" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AUMReinsuranceSegmentMember_019dcdb8-9e2d-74c6-8211-64ef81abfd8b_terseLabel_en-US" xlink:label="lab_kg_AUMReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AUM Reinsurance Segment</link:label>
    <link:label id="lab_kg_AUMReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_AUMReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AUM Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_AUMReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_AUMReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AUM Reinsurance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AUMReinsuranceSegmentMember" xlink:href="kg-20260331.xsd#kg_AUMReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AUMReinsuranceSegmentMember" xlink:to="lab_kg_AUMReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentHoldingsTextBlock_019ce734-5ba0-7848-b17c-fecbd4fe31b5_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments</link:label>
    <link:label id="lab_us-gaap_InvestmentHoldingsTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentHoldingsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Holdings [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentHoldingsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentHoldingsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentHoldingsTextBlock" xlink:to="lab_us-gaap_InvestmentHoldingsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceDisclosuresAbstract_019ce734-5c52-7733-ab6b-7616abc7f148_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_ReinsuranceDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_ReinsuranceDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceDisclosuresAbstract" xlink:to="lab_us-gaap_ReinsuranceDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementLineItems_019ce734-5ba0-7151-b1e5-9b35d63a9cc2_terseLabel_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:label id="lab_us-gaap_StatementLineItems_label_en-US" xlink:label="lab_us-gaap_StatementLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementLineItems" xlink:to="lab_us-gaap_StatementLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted</link:label>
    <link:label id="lab_ecd_Rule10b51ArrAdoptedFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Adopted [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrAdoptedFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrAdoptedFlag" xlink:to="lab_ecd_Rule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019ce734-5c52-7035-854b-d3a3cd1a667b_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_019ce734-5c52-75a6-a0c0-bbe2e4d68fca_verboseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsAtCarryingValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:to="lab_us-gaap_CashAndCashEquivalentsAtCarryingValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ShareRepurchasePlanMember_019ce734-5ba1-7464-a311-ddfc21e1ce5b_terseLabel_en-US" xlink:label="lab_kg_ShareRepurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Plan</link:label>
    <link:label id="lab_kg_ShareRepurchasePlanMember_label_en-US" xlink:label="lab_kg_ShareRepurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Plan [Member]</link:label>
    <link:label id="lab_kg_ShareRepurchasePlanMember_documentation_en-US" xlink:label="lab_kg_ShareRepurchasePlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share Repurchase Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareRepurchasePlanMember" xlink:href="kg-20260331.xsd#kg_ShareRepurchasePlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShareRepurchasePlanMember" xlink:to="lab_kg_ShareRepurchasePlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockMember_019ce734-5ba0-7a63-afb0-4971b7b9dfb1_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_019ce734-5ba0-7520-baa5-3f887d62d45d_verboseLabel_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Privately held common stocks</link:label>
    <link:label id="lab_us-gaap_CommonStockMember_label_en-US" xlink:label="lab_us-gaap_CommonStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockMember" xlink:to="lab_us-gaap_CommonStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_019ce734-5c52-7beb-a130-39e0334f77e0_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net increase (decrease) in cash, restricted cash and cash equivalents</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_019ce734-5ba0-75e6-8b8b-9e5ccdb42aa4_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Potentially dilutive securities (in shares)</link:label>
    <link:label id="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Diluted, Adjustment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:to="lab_us-gaap_WeightedAverageNumberDilutedSharesOutstandingAdjustment" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_019ce734-5c52-7459-b66b-8540aaac4409_terseLabel_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies</link:label>
    <link:label id="lab_us-gaap_SignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_SignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_019ce734-5cd9-7760-a921-5493b801518e_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums and losses related to policies, percentage</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Premiums and Losses Related to Policies</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Premiums and Losses Related to Policies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:to="lab_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_RangeMember_019ce734-5c52-788e-b091-77b12f31c53e_terseLabel_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:label id="lab_srt_RangeMember_label_en-US" xlink:label="lab_srt_RangeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statistical Measurement [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeMember"/>
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    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_019ce734-5c52-712b-a583-c185d158b74f_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related party transaction, percentage of required funding on obligations</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Required Funding On Obligations</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percentage Of Required Funding On Obligations</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_019ce734-5cd9-7b3c-9440-00464e25dadb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Allowance for expected credit losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Allowance for Credit Loss, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff"/>
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    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_019ce734-5c52-733c-bd86-2f8524661c5c_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net incurred losses related to Prior years</link:label>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Prior Year Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense"/>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_019d3d0b-47b8-75ed-8c9e-3f644701ec82_verboseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2026</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_019ce734-5c52-78e7-92ff-49d74206256e_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_019ce734-5ba0-76dc-bac5-564caff507d3_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:label id="lab_us-gaap_ValuationTechniqueDomain_label_en-US" xlink:label="lab_us-gaap_ValuationTechniqueDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Approach and Technique [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationTechniqueDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationTechniqueDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationTechniqueDomain" xlink:to="lab_us-gaap_ValuationTechniqueDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_019ce734-5c52-783b-be4f-106cda30f14b_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized gains during the period</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Measurement with Unobservable Inputs Reconciliation, Recurring Basis, Asset, Gain (Loss) Included in Other Comprehensive Income (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss"/>
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    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019ce734-5ba0-7d73-a694-8e2dd0fc8a28_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest in loss of equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_019ce734-5ba0-76a4-95f4-100baeff1e9f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Interest in loss of equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:to="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_019ce734-5ba1-7db6-ab43-ed08d92bd882_negatedTerseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Equity portion of consideration transferred to Maiden Reinsurance</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest in Treasury Stock</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest in Treasury Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:href="kg-20260331.xsd#kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredEquityInterestInTreasuryStock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnearnedPremiums_019ce734-5c52-7a8f-9c44-0ba8719750e2_verboseLabel_en-US" xlink:label="lab_us-gaap_UnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums (includes $16,815 and $17,227 from related parties in 2026 and 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_UnearnedPremiums_019ce734-5c52-76e5-90a9-defdac5dab15_terseLabel_en-US" xlink:label="lab_us-gaap_UnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums</link:label>
    <link:label id="lab_us-gaap_UnearnedPremiums_label_en-US" xlink:label="lab_us-gaap_UnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unearned Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnearnedPremiums" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnearnedPremiums"/>
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    <link:label id="lab_kg_KILHMember_019ce734-5c52-748d-9dcc-23393c6f0593_terseLabel_en-US" xlink:label="lab_kg_KILHMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">KILH</link:label>
    <link:label id="lab_kg_KILHMember_label_en-US" xlink:label="lab_kg_KILHMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">KILH [Member]</link:label>
    <link:label id="lab_kg_KILHMember_documentation_en-US" xlink:label="lab_kg_KILHMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">KILH</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KILHMember" xlink:href="kg-20260331.xsd#kg_KILHMember"/>
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    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_019ce734-5c52-7ade-bc5e-0b6bc1f194e4_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible Asset, Acquired, Finite-Lived [Line Items]</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Intangible Asset, Acquired, Finite-Lived [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019ce734-5cd9-7b8e-8ca7-8ee915d25426_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_019ce734-5cd9-7d00-a945-c80e35374b46_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group Ltd shares issued at Closing (in shares)</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest, Share Issued, Number of Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionEquityInterestsIssuedOrIssuableNumberOfSharesIssued"/>
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    <link:label id="lab_us-gaap_GainContingenciesLineItems_019ce734-5c52-7349-a58d-1eecdb50ecc7_terseLabel_en-US" xlink:label="lab_us-gaap_GainContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_GainContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_GainContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainContingenciesLineItems"/>
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    <link:label id="lab_ecd_TradingArrByIndTable_terseLabel_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual</link:label>
    <link:label id="lab_ecd_TradingArrByIndTable_label_en-US" xlink:label="lab_ecd_TradingArrByIndTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangements, by Individual [Table]</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareBasic_019ce734-5c52-7f14-9240-88e7e4d2e055_totalLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Basic loss per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareBasic_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share, Basic</link:label>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward_019ce734-5c52-7614-8c41-f1f44a7659b8_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward"/>
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    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_019ce734-5c52-7110-bdf3-8dd8580ae54c_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount rate</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountRateMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount Rate [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountRateMember" xlink:to="lab_us-gaap_MeasurementInputDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_019ce734-5c52-720e-9499-5d9a0ac94de5_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Reportable Segments Underwriting Results to Consolidated Net Loss</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Segment Reporting Information, by Segment [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock"/>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_019ce734-5c52-775f-81eb-864b7b5236a6_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted loss from discontinued operations per share attributable to Kestrel common shareholders (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Discontinued Operations and Disposal of Discontinued Operations, Net of Tax, Per Diluted Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxPerDilutedShare"/>
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    <link:label id="lab_kg_InterestAndAmortizationExpensesNet_019ce734-5c52-7c17-9a8b-016f3588c7c7_terseLabel_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest and amortization expenses</link:label>
    <link:label id="lab_kg_InterestAndAmortizationExpensesNet_019ce734-5c52-7bdf-adef-422e6f8aee04_negatedLabel_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Interest and amortization expenses</link:label>
    <link:label id="lab_kg_InterestAndAmortizationExpensesNet_label_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest and Amortization Expenses, Net</link:label>
    <link:label id="lab_kg_InterestAndAmortizationExpensesNet_documentation_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Interest and Amortization Expenses, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InterestAndAmortizationExpensesNet" xlink:href="kg-20260331.xsd#kg_InterestAndAmortizationExpensesNet"/>
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    <link:label id="lab_us-gaap_MeasurementInputTypeDomain_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeDomain"/>
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    <link:label id="lab_srt_AffiliatedEntityMember_019ce734-5cd9-7284-ae88-2cad752e0f69_terseLabel_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Affiliated Entity</link:label>
    <link:label id="lab_srt_AffiliatedEntityMember_label_en-US" xlink:label="lab_srt_AffiliatedEntityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Affiliated Entity [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_AffiliatedEntityMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_AffiliatedEntityMember"/>
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    <link:label id="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_019ce734-5cd9-7bbf-9434-c95b248b5cb1_terseLabel_en-US" xlink:label="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total unfunded commitments on alternative investments</link:label>
    <link:label id="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_label_en-US" xlink:label="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments And Equity Method Investments [Member]</link:label>
    <link:label id="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_documentation_en-US" xlink:label="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Investments And Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:href="kg-20260331.xsd#kg_OtherInvestmentsAndEquityMethodInvestmentsMember"/>
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    <link:label id="lab_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember_019d33da-9605-7f27-8b44-19fd0fe98491_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discount for Lack of Marketability</link:label>
    <link:label id="lab_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Discount for Lack of Marketability [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember"/>
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    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_019ce734-5cd9-734a-8964-dc5551069948_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">12 Months or More</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Twelve Months or Longer, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Twelve Months or Longer, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionTwelveMonthsorLongerFairValue"/>
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    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_019ce734-5c52-762d-8b02-efaf71086d36_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Other general and administrative expenses</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherGeneralAndAdministrativeExpense"/>
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    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss_019ce734-5c52-74da-8c29-0502571f1831_negatedTotalLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionAccumulatedLoss"/>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireEquityMethodInvestments"/>
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    <link:label id="lab_us-gaap_SegmentReportingAssetReconcilingItemLineItems_019ce734-5c52-7179-833b-0e74b4fdc4c3_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAssetReconcilingItemLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Asset Reconciling Item [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAssetReconcilingItemLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAssetReconcilingItemLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Asset Reconciling Item [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAssetReconcilingItemLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAssetReconcilingItemLineItems"/>
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    <link:label id="lab_kg_InvestmentsInDirectLendingEntitiesMember_019d33da-9605-7ce5-8b28-ed0b49e54150_terseLabel_en-US" xlink:label="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment in direct lending entities</link:label>
    <link:label id="lab_kg_InvestmentsInDirectLendingEntitiesMember_label_en-US" xlink:label="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments In Direct Lending Entities [Member]</link:label>
    <link:label id="lab_kg_InvestmentsInDirectLendingEntitiesMember_documentation_en-US" xlink:label="lab_kg_InvestmentsInDirectLendingEntitiesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments In Direct Lending Entities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsInDirectLendingEntitiesMember" xlink:href="kg-20260331.xsd#kg_InvestmentsInDirectLendingEntitiesMember"/>
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    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_019d3d39-fa85-752c-97e1-96c2b471b8b7_terseLabel_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense: fair value discount on net reserves acquired</link:label>
    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_label_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Discount on Acquired Reserves [Member]</link:label>
    <link:label id="lab_kg_FairValueDiscountOnAcquiredReservesMember_documentation_en-US" xlink:label="lab_kg_FairValueDiscountOnAcquiredReservesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fair Value Discount on Acquired Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FairValueDiscountOnAcquiredReservesMember" xlink:href="kg-20260331.xsd#kg_FairValueDiscountOnAcquiredReservesMember"/>
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    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_019ce734-5cd9-72b0-b60e-469c92ae044e_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities and equity</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAndStockholdersEquity_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAndStockholdersEquity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities and Equity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAndStockholdersEquity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAndStockholdersEquity"/>
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    <link:label id="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_label_en-US" xlink:label="lab_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_019dcdb8-9e2d-7c1e-ac45-b5422524ef19_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByBenchmarkAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByBenchmarkAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:to="lab_us-gaap_ConcentrationRiskByBenchmarkAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember_019ce734-5c52-739b-a297-1c34e8028863_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Maximum Loss Corridor</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Maximum Loss Corridor [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Maximum Loss Corridor [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:href="kg-20260331.xsd#kg_PostTerminationEndorsementMaximumLossCorridorMember"/>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_019ce734-5c52-7c17-a52c-3218aa0812db_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsIncludingDisposalGroupAndDiscontinuedOperations"/>
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    <link:label id="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_019ce734-5cd9-768d-bfb1-b0fd227c357a_terseLabel_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assets, valued by third party, percentage</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_label_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Valued by Third Party, Percentage</link:label>
    <link:label id="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_documentation_en-US" xlink:label="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure, Valued by Third Party, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:href="kg-20260331.xsd#kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage"/>
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    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseMember_019ddf80-7b92-7a6d-9a7d-eee880ee884e_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and Administrative Expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpenseMember_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpenseMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpenseMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_019ce734-5c52-7dcb-92cb-3975a5f985b8_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Equity Method Investments [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEquityMethodInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfEquityMethodInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_019ce734-5c52-7572-9754-096cd94376b5_terseLabel_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:label id="lab_us-gaap_AccountingPoliciesAbstract_label_en-US" xlink:label="lab_us-gaap_AccountingPoliciesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accounting Policies [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccountingPoliciesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccountingPoliciesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccountingPoliciesAbstract" xlink:to="lab_us-gaap_AccountingPoliciesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_019ce734-5cd9-75e8-9444-f6c76b934b75_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scheduled of Maturity of Operating Lease Liabilities</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Maturity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityMaturityTableTextBlock"/>
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    <link:label id="lab_us-gaap_ConcentrationRiskTypeDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTypeDomain"/>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:href="kg-20260331.xsd#kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_019ce734-5c52-74f3-b047-4cd57a18274f_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of other investments</link:label>
    <link:label id="lab_us-gaap_PaymentsToAcquireOtherInvestments_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireOtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireOtherInvestments" xlink:to="lab_us-gaap_PaymentsToAcquireOtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_019ce734-5cd9-73bd-b039-c3847dc75861_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss from continuing operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Net of Tax, Including Portion Attributable to Noncontrolling Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsIncludingPortionAttributableToNoncontrollingInterest" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_019ce734-5c52-78bf-bb2b-6d9c6fef7d11_terseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Treasury shares</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonMember_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockCommonMember" xlink:to="lab_us-gaap_TreasuryStockCommonMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PayVsPerformanceDisclosureLineItems_label_en-US" xlink:label="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PayVsPerformanceDisclosureLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PayVsPerformanceDisclosureLineItems" xlink:to="lab_ecd_PayVsPerformanceDisclosureLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_019d33da-9605-7ad3-9f72-8524e61a614e_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Receivable, measurement inputs</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_label_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Asset, Measurement Input</link:label>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_documentation_en-US" xlink:label="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Asset, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:href="kg-20260331.xsd#kg_BusinessCombinationContingentConsiderationAssetMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:to="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019ce734-5cd9-7da9-a7fa-efcbb6d34da0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, liability</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_019ce734-5cd9-7580-bfff-1983da2bac74_totalLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total discounted operating lease liabilities</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiability_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiability" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiability" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiability"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiability" xlink:to="lab_us-gaap_OperatingLeaseLiability" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_019ce734-5ba0-7ae8-9c90-e3d574b136e3_terseLabel_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. agency bonds&#160;&#8211;&#160;mortgage-backed</link:label>
    <link:label id="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Government Agencies Debt Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USGovernmentAgenciesDebtSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:to="lab_us-gaap_USGovernmentAgenciesDebtSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums_019ce734-5cd9-7492-a1e5-68ab41e120db_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Unearned Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInUnearnedPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:to="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_019ce734-5ba0-7ac3-8b0e-5d73dff13f7d_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LIABILITIES</link:label>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_LiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesAbstract" xlink:to="lab_us-gaap_LiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_019ce734-5ba0-7f44-8a66-5baf31124e61_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:to="lab_us-gaap_BusinessCombinationDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_019ce734-5cd9-75d2-93fb-f638470ed73a_terseLabel_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Senior Notes</link:label>
    <link:label id="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Liabilities Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancialLiabilitiesFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:to="lab_us-gaap_FinancialLiabilitiesFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ProgramServicesSegmentMember_019ce734-5c52-78a4-b398-c80d137fe5fc_terseLabel_en-US" xlink:label="lab_kg_ProgramServicesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Program Services</link:label>
    <link:label id="lab_kg_ProgramServicesSegmentMember_label_en-US" xlink:label="lab_kg_ProgramServicesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Program Services Segment [Member]</link:label>
    <link:label id="lab_kg_ProgramServicesSegmentMember_documentation_en-US" xlink:label="lab_kg_ProgramServicesSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Program Services Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ProgramServicesSegmentMember" xlink:href="kg-20260331.xsd#kg_ProgramServicesSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ProgramServicesSegmentMember" xlink:to="lab_kg_ProgramServicesSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_019ce734-5ba0-70de-9c0a-d33c0206f9ab_terseLabel_en-US" xlink:label="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative arrangement, payment of commuted reserves</link:label>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_label_en-US" xlink:label="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Payment of Commuted Reserves</link:label>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_documentation_en-US" xlink:label="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Payment of Commuted Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:href="kg-20260331.xsd#kg_CollaborativeArrangementPaymentOfCommutedReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:to="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember_019d33da-9605-751b-91dc-8929628dd7f3_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">EBITDA &amp; Commission Discount Rate</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember_label_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Discount Rate [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, EBITDA and Commission Discount Rate</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:href="kg-20260331.xsd#kg_MeasurementInputEBITDAAndCommissionDiscountRateMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:to="lab_kg_MeasurementInputEBITDAAndCommissionDiscountRateMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_019ce734-5cd9-7fed-8cdf-90a7415ecd25_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation, Calculation [Roll Forward]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:to="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_019ce734-5ba1-7fed-8b29-74738d13fffc_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Variable Interest Entities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfVariableInterestEntitiesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:to="lab_us-gaap_ScheduleOfVariableInterestEntitiesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_019ce734-5cd9-7d41-9cd4-8c99ef9d2cbc_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfCashFlowsAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Cash Flows [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfCashFlowsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfCashFlowsAbstract" xlink:to="lab_us-gaap_StatementOfCashFlowsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:label id="lab_ecd_CoSelectedMeasureAmt_label_en-US" xlink:label="lab_ecd_CoSelectedMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Company Selected Measure Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_CoSelectedMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_CoSelectedMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_CoSelectedMeasureAmt" xlink:to="lab_ecd_CoSelectedMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_019ce734-5ba0-757a-a9f6-30ae96dc5688_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2029</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_019ce734-5c52-70b7-b8a7-97c93e9ac1c2_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Original fair value adjustment at acquisition date</link:label>
    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_label_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Issuance Costs, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredFinanceCostsGross" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredFinanceCostsGross"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredFinanceCostsGross" xlink:to="lab_us-gaap_DeferredFinanceCostsGross" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_019ce734-5c52-7956-8b49-8536b8a20c6f_totalLabel_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Comprehensive loss</link:label>
    <link:label id="lab_us-gaap_ComprehensiveIncomeNetOfTax_label_en-US" xlink:label="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Comprehensive Income (Loss), Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ComprehensiveIncomeNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ComprehensiveIncomeNetOfTax" xlink:to="lab_us-gaap_ComprehensiveIncomeNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_019ce734-5ba0-718b-bafe-f5238311f432_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:label id="lab_us-gaap_MeasurementInputTypeAxis_label_en-US" xlink:label="lab_us-gaap_MeasurementInputTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputTypeAxis" xlink:to="lab_us-gaap_MeasurementInputTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MeasureName_terseLabel_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_MeasureName_label_en-US" xlink:label="lab_ecd_MeasureName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measure Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MeasureName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MeasureName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_MeasureName" xlink:to="lab_ecd_MeasureName" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_019ce734-5ba0-795a-b843-18b2ff83d419_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Reinsurance Recoverable on Unpaid Losses</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Reinsurance Recoverable on Unpaid Losses</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_019ce734-5cd9-7ffa-9d98-4612381d067c_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Due in one year or less</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Maturity, Allocated and Single Maturity Date, Year One</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_019ce734-5c52-7deb-8423-e4b915dcd1b7_totalLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss, before tax</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_019ce734-5cd9-71c9-b3ef-d1f35e980169_terseLabel_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:label id="lab_us-gaap_ClassOfStockLineItems_label_en-US" xlink:label="lab_us-gaap_ClassOfStockLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Stock [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ClassOfStockLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ClassOfStockLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ClassOfStockLineItems" xlink:to="lab_us-gaap_ClassOfStockLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsOriginalOrAmortizedCostBasis_019ce734-5cd9-7ab5-9719-eb25e3a852c9_terseLabel_en-US" xlink:label="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_kg_InvestmentsOriginalOrAmortizedCostBasis_label_en-US" xlink:label="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Original or Amortized Cost Basis</link:label>
    <link:label id="lab_kg_InvestmentsOriginalOrAmortizedCostBasis_documentation_en-US" xlink:label="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Original or Amortized Cost Basis</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:href="kg-20260331.xsd#kg_InvestmentsOriginalOrAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:to="lab_kg_InvestmentsOriginalOrAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsFairValueOptionMember_019ce734-5c52-7e8d-89ec-60e9b841ca4a_terseLabel_en-US" xlink:label="lab_kg_InvestmentsFairValueOptionMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total equity method investments with fair value option</link:label>
    <link:label id="lab_kg_InvestmentsFairValueOptionMember_label_en-US" xlink:label="lab_kg_InvestmentsFairValueOptionMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Option [Member]</link:label>
    <link:label id="lab_kg_InvestmentsFairValueOptionMember_documentation_en-US" xlink:label="lab_kg_InvestmentsFairValueOptionMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Option</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentsFairValueOptionMember" xlink:href="kg-20260331.xsd#kg_InvestmentsFairValueOptionMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsFairValueOptionMember" xlink:to="lab_kg_InvestmentsFairValueOptionMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_019ce734-5cd9-7084-be96-abab06e49240_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss from discontinued operations, net of income tax</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_019ce734-5cd9-770d-870e-9d4156a9617a_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Less: net loss from discontinued operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_019ce734-5cd9-7577-8a08-e6b43d41dcd4_negatedLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Loss from discontinued operations, net of income tax</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_019ce734-5cd9-73f8-95cc-a3b216a9fe59_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss from discontinued operations</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Discontinued Operations, Net of Tax, Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTaxAttributableToReportingEntity"/>
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    <link:label id="lab_us-gaap_AssumedPremiumsWritten_019ce734-5c52-7994-8669-5f6a557de676_terseLabel_en-US" xlink:label="lab_us-gaap_AssumedPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Assumed</link:label>
    <link:label id="lab_us-gaap_AssumedPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_AssumedPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assumed Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssumedPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssumedPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssumedPremiumsWritten" xlink:to="lab_us-gaap_AssumedPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_019ce734-5ba0-784c-81c4-f3d37922ce03_terseLabel_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Unrealized Losses Included in Accumulated Other Comprehensive Income</link:label>
    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_label_en-US" xlink:label="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrealized Gain (Loss) on Investments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock"/>
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    <link:label id="lab_kg_FixedMaturitiesFairValue_019ce734-5c52-72f9-a729-2af222a734bd_verboseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_kg_FixedMaturitiesFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesFairValue" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesFairValue"/>
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    <link:label id="lab_us-gaap_LongTermDebt_019ce734-5ba0-7459-9855-d3661a2ef5d1_totalLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Senior notes, net</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_019ce734-5ba0-72bb-a03c-2d0591779dc3_terseLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Carrying value</link:label>
    <link:label id="lab_us-gaap_LongTermDebt_label_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongTermDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongTermDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongTermDebt" xlink:to="lab_us-gaap_LongTermDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LegalEntityAxis_019ce734-5ba0-73b9-86d4-683eaef230ba_terseLabel_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:label id="lab_dei_LegalEntityAxis_label_en-US" xlink:label="lab_dei_LegalEntityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Legal Entity [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LegalEntityAxis" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LegalEntityAxis"/>
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    <link:label id="lab_us-gaap_Assets_019ce734-5cd9-77ea-8840-1a774f40bf8b_totalLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total assets</link:label>
    <link:label id="lab_us-gaap_Assets_label_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Assets" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Assets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Assets" xlink:to="lab_us-gaap_Assets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019d3d3a-b9f3-77fc-a917-39562ec52229_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2027</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_019d33da-9605-733f-8b42-3946a0c473d2_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 3</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ThirdPartyAgreementsMember_019ce734-5c52-7039-8e47-a7a9c0666df5_terseLabel_en-US" xlink:label="lab_kg_ThirdPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Third Party Agreements</link:label>
    <link:label id="lab_kg_ThirdPartyAgreementsMember_label_en-US" xlink:label="lab_kg_ThirdPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Third Party Agreements [Member]</link:label>
    <link:label id="lab_kg_ThirdPartyAgreementsMember_documentation_en-US" xlink:label="lab_kg_ThirdPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Third Party Agreements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ThirdPartyAgreementsMember" xlink:href="kg-20260331.xsd#kg_ThirdPartyAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ThirdPartyAgreementsMember" xlink:to="lab_kg_ThirdPartyAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_019ce734-5cd9-74f1-9ee3-9f044d1c9582_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from operating activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceCollateralByThirdParty_019ce734-5cd9-7337-ad0f-c492f3fc2592_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceCollateralByThirdParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral by third party</link:label>
    <link:label id="lab_kg_ReinsuranceCollateralByThirdParty_label_en-US" xlink:label="lab_kg_ReinsuranceCollateralByThirdParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Collateral By Third Party</link:label>
    <link:label id="lab_kg_ReinsuranceCollateralByThirdParty_documentation_en-US" xlink:label="lab_kg_ReinsuranceCollateralByThirdParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance, Collateral By Third Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceCollateralByThirdParty" xlink:href="kg-20260331.xsd#kg_ReinsuranceCollateralByThirdParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceCollateralByThirdParty" xlink:to="lab_kg_ReinsuranceCollateralByThirdParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock_019ce734-5ba0-7f55-aca0-c010f19a2fd3_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements Disclosure and Significant Accounting Policies [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureAndSignificantAccountingPoliciesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_019d3d3c-4b59-7766-8961-d599f9063b16_terseLabel_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period</link:label>
    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife_label_en-US" xlink:label="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Acquired Finite-Lived Intangible Assets, Weighted Average Useful Life</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:to="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsWeightedAverageUsefulLife" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_019dcdb8-9e2d-7cb4-ad50-80358a7104b0_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Type [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskByTypeAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskByTypeAxis" xlink:to="lab_us-gaap_ConcentrationRiskByTypeAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivateEquityFundsMember_019ce734-5ba0-7228-9d11-3d208e9cefa8_terseLabel_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity funds</link:label>
    <link:label id="lab_us-gaap_PrivateEquityFundsMember_label_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Private Equity Funds [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PrivateEquityFundsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PrivateEquityFundsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PrivateEquityFundsMember" xlink:to="lab_us-gaap_PrivateEquityFundsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019d3d3a-b9f3-78ef-9083-1d8abfc98e23_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_019ce734-5cd9-7a58-848f-bcd5c641d675_terseLabel_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:label id="lab_us-gaap_VariableInterestEntityLineItems_label_en-US" xlink:label="lab_us-gaap_VariableInterestEntityLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Variable Interest Entity [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VariableInterestEntityLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VariableInterestEntityLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VariableInterestEntityLineItems" xlink:to="lab_us-gaap_VariableInterestEntityLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherInvestments_019ce734-5ba0-7f13-8d98-8a62825a7580_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_019ce734-5ba0-7f8a-836d-85f73bff1443_verboseLabel_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Total other investments at fair value</link:label>
    <link:label id="lab_us-gaap_OtherInvestments_label_en-US" xlink:label="lab_us-gaap_OtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInvestments" xlink:to="lab_us-gaap_OtherInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_019ce734-5c52-7e56-a317-d9bcf42adedc_terseLabel_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:label id="lab_dei_EntityCommonStockSharesOutstanding_label_en-US" xlink:label="lab_dei_EntityCommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Common Stock, Shares Outstanding</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityCommonStockSharesOutstanding" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityCommonStockSharesOutstanding"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityCommonStockSharesOutstanding" xlink:to="lab_dei_EntityCommonStockSharesOutstanding" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_019ce734-5ba1-757a-b9be-5ea920357d3d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-sale [Line Items]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:to="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019ce734-5ba0-757c-898e-85c3e17fde62_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Significant Other Observable Inputs (Level 2)</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_019ce734-5ba0-7349-b9f8-361f136be178_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2</link:label>
    <link:label id="lab_us-gaap_FairValueInputsLevel2Member_label_en-US" xlink:label="lab_us-gaap_FairValueInputsLevel2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Inputs, Level 2 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInputsLevel2Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInputsLevel2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueInputsLevel2Member" xlink:to="lab_us-gaap_FairValueInputsLevel2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestments_019ce734-5cd9-755c-8aba-47a424d50fdb_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Carrying Value</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestments" xlink:to="lab_us-gaap_EquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted</link:label>
    <link:label id="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock_label_en-US" xlink:label="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Policies and Procedures Not Adopted [Text Block]</link:label>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_019ce734-5c52-7229-bb96-d0d29228921e_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAcquireeDomain"/>
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    <link:label id="lab_kg_RelatedPartyAgreementsMember_019ce734-5ba0-7650-a7c5-a7e0337cd351_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Agreements</link:label>
    <link:label id="lab_kg_RelatedPartyAgreementsMember_label_en-US" xlink:label="lab_kg_RelatedPartyAgreementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Agreements [Member]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyAgreementsMember" xlink:href="kg-20260331.xsd#kg_RelatedPartyAgreementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyAgreementsMember" xlink:to="lab_kg_RelatedPartyAgreementsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019ce734-5cd9-70d6-b97b-dba33f0afc0e_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments with fair value option elected</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019ce734-5cd9-7293-ab7f-5c4e8c0c98c6_netLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total unfunded commitments on equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019ce734-5cd9-7979-bf9d-11ca097d082e_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentsMember" xlink:to="lab_us-gaap_EquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameAxis_019ce734-5c52-7016-a4e7-3e0ad792b5f1_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:label id="lab_us-gaap_PlanNameAxis_label_en-US" xlink:label="lab_us-gaap_PlanNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameAxis" xlink:to="lab_us-gaap_PlanNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoMember_terseLabel_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO</link:label>
    <link:label id="lab_ecd_PeoMember_label_en-US" xlink:label="lab_ecd_PeoMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoMember" xlink:to="lab_ecd_PeoMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ExtellHudsonWaterfrontHoldingsMember_019ce734-5cd9-74e3-ad42-752b820308be_terseLabel_en-US" xlink:label="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings</link:label>
    <link:label id="lab_kg_ExtellHudsonWaterfrontHoldingsMember_label_en-US" xlink:label="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings [Member]</link:label>
    <link:label id="lab_kg_ExtellHudsonWaterfrontHoldingsMember_documentation_en-US" xlink:label="lab_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Extell Hudson Waterfront Holdings</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ExtellHudsonWaterfrontHoldingsMember" xlink:href="kg-20260331.xsd#kg_ExtellHudsonWaterfrontHoldingsMember"/>
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    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_019ce734-5cd9-7d18-a8e8-1db1faa28ee0_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Contractual Maturities of Fixed Maturities</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations before Equity Method Investments, Income Taxes, Noncontrolling Interest</link:label>
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    <link:label id="lab_country_US_019d3d25-001e-7233-b3b7-a1c9985dd8f1_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_019ce734-5c52-7ae3-9d91-e4d680168aca_terseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Retained earnings (accumulated deficit)</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsMember_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsMember" xlink:to="lab_us-gaap_RetainedEarningsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense_019ce734-5c52-73ea-9335-5692f78c3bfc_negatedTotalLabel_en-US" xlink:label="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel" xlink:type="resource" xml:lang="en-US">Net paid losses</link:label>
    <link:label id="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Claims Paid</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:to="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_019ce734-5c52-78b2-b51f-f5789fd7fd42_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Authority [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_label_en-US" xlink:label="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Jurisdiction [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxAuthorityAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxAuthorityAxis" xlink:to="lab_us-gaap_IncomeTaxAuthorityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ce734-5cd9-7786-b969-7b74279f1d18_periodStartLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, beginning of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ce734-5cd9-7a5a-8b57-ef1814345347_periodEndLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Cash, restricted cash and cash equivalents, end of period, excluding held-for-sale</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_019ce734-5cd9-7324-b183-666cbdf310e2_totalLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total cash, restricted cash and cash equivalents, end of period</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents"/>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_019ce734-5c52-7358-a0b3-c759df098363_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Income (Loss)</link:label>
    <link:label id="lab_us-gaap_IncomeStatementAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeStatementAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementAbstract"/>
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    <link:label id="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent_019ce734-5ba0-7789-9169-de50c474373f_terseLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive (loss) income before reclassifications</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OciBeforeReclassificationsBeforeTaxAttributableToParent"/>
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    <link:label id="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract_label_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsWrittenNetConsolidatedAbstract"/>
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    <link:label id="lab_us-gaap_PaymentsToAcquireMarketableSecurities_label_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments to Acquire Marketable Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsToAcquireMarketableSecurities"/>
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    <link:label id="lab_us-gaap_InvestmentsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_InvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments, Fair Value Disclosure</link:label>
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    <link:label id="lab_srt_ProductsAndServicesDomain_019ce734-5cd9-7a91-962f-6da14f5a76b2_terseLabel_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2016Member" xlink:href="kg-20260331.xsd#kg_SeniorNotes2016Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SeniorNotes2016Member" xlink:to="lab_kg_SeniorNotes2016Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_019ce734-5ba0-7c67-87cf-8227fbf3f65c_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Diluted loss from continuing operations per share attributable to Kestrel common shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_019ce734-5ba0-788c-9810-a7888e4e9a93_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Diluted loss from continuing operations per share attributable to Kestrel shareholders (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_label_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income (Loss) from Continuing Operations, Per Diluted Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare" xlink:to="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_019ce734-5c52-7d3e-9f89-ea3b61955618_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance, excess retention, amount reinsured, per policy</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Excess Retention, Amount Reinsured, Per Policy</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:to="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_019d33da-9605-7b90-a7f3-2f18cbc0c326_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, measurement input</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:to="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_terseLabel_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement does not require Recovery</link:label>
    <link:label id="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock_label_en-US" xlink:label="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Does Not Require Recovery [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDoesNotRequireRecoveryTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:to="lab_ecd_RestatementDoesNotRequireRecoveryTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_019ce734-5c52-7faa-83d1-52e25080d26b_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_019ce734-5cd9-7189-bc82-3571cc2392c9_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_label_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:to="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_019ce734-5c52-7256-9fdf-217219e83bae_terseLabel_en-US" xlink:label="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Prior notice to be given before redemption date</link:label>
    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_label_en-US" xlink:label="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prior Notice, Redemption Period, Start Date</link:label>
    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_documentation_en-US" xlink:label="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Debt Instrument, Prior Notice, Redemption Period, Start Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:href="kg-20260331.xsd#kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:to="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_019ce734-5c52-7ac8-97a5-d8679a163c72_terseLabel_en-US" xlink:label="lab_kg_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of votes per share</link:label>
    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_label_en-US" xlink:label="lab_kg_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Number Of Votes Per Share</link:label>
    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_documentation_en-US" xlink:label="lab_kg_CommonStockNumberOfVotesPerShare" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Number Of Votes Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockNumberOfVotesPerShare" xlink:href="kg-20260331.xsd#kg_CommonStockNumberOfVotesPerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommonStockNumberOfVotesPerShare" xlink:to="lab_kg_CommonStockNumberOfVotesPerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_019ce734-5cd9-785d-aed4-3bba58176221_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Purchase Price of Assets and Liabilities Assumed</link:label>
    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired and Liability Assumed [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_019ce734-5cd9-7907-9255-0806f9cd43e3_terseLabel_en-US" xlink:label="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lease payments to escalating fee, percentage</link:label>
    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_label_en-US" xlink:label="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Escalating Fee Percentage</link:label>
    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_documentation_en-US" xlink:label="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Operating Lease, Escalating Fee Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OperatingLeaseEscalatingFeePercentage" xlink:href="kg-20260331.xsd#kg_OperatingLeaseEscalatingFeePercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OperatingLeaseEscalatingFeePercentage" xlink:to="lab_kg_OperatingLeaseEscalatingFeePercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_CityAreaCode_019ce734-5cd9-724c-92dd-659dbec614af_terseLabel_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:label id="lab_dei_CityAreaCode_label_en-US" xlink:label="lab_dei_CityAreaCode" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">City Area Code</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_CityAreaCode" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_CityAreaCode"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_CityAreaCode" xlink:to="lab_dei_CityAreaCode" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered</link:label>
    <link:label id="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock_label_en-US" xlink:label="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing, How MNPI Considered [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardTmgHowMnpiCnsdrdTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:to="lab_ecd_AwardTmgHowMnpiCnsdrdTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AUMFinancialServicesInc.Member_019dcdb8-9e2d-758e-b85b-d91e7c5e40e0_terseLabel_en-US" xlink:label="lab_kg_AUMFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AUM Financial Services, Inc.</link:label>
    <link:label id="lab_kg_AUMFinancialServicesInc.Member_label_en-US" xlink:label="lab_kg_AUMFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AUM Financial Services, Inc. [Member]</link:label>
    <link:label id="lab_kg_AUMFinancialServicesInc.Member_documentation_en-US" xlink:label="lab_kg_AUMFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AUM Programs Financial Services, Inc.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AUMFinancialServicesInc.Member" xlink:href="kg-20260331.xsd#kg_AUMFinancialServicesInc.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AUMFinancialServicesInc.Member" xlink:to="lab_kg_AUMFinancialServicesInc.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_019d3d3d-27cb-7d61-8e83-3e8fa774b5a2_terseLabel_en-US" xlink:label="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period</link:label>
    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_label_en-US" xlink:label="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period [Abstract]</link:label>
    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_documentation_en-US" xlink:label="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Weighted Average Amortization Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_WeightedAverageAmortizationPeriodAbstract" xlink:href="kg-20260331.xsd#kg_WeightedAverageAmortizationPeriodAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_WeightedAverageAmortizationPeriodAbstract" xlink:to="lab_kg_WeightedAverageAmortizationPeriodAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_019ce734-5c52-72b3-8dbf-8218d1eca1ee_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:to="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_019ce734-5cd9-744a-b1ec-eae37ccf984a_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from investing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_019ce734-5ba0-7772-9609-6510e072e1c0_terseLabel_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_GeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_GeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupLtd.Member_019ce734-5cd9-794f-87e8-2a1127b4d3f5_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupLtd.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group, Ltd.</link:label>
    <link:label id="lab_kg_KestrelGroupLtd.Member_label_en-US" xlink:label="lab_kg_KestrelGroupLtd.Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Group, Ltd. [Member]</link:label>
    <link:label id="lab_kg_KestrelGroupLtd.Member_documentation_en-US" xlink:label="lab_kg_KestrelGroupLtd.Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Group, Ltd.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLtd.Member" xlink:href="kg-20260331.xsd#kg_KestrelGroupLtd.Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupLtd.Member" xlink:to="lab_kg_KestrelGroupLtd.Member" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PvpTable_terseLabel_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure</link:label>
    <link:label id="lab_ecd_PvpTable_label_en-US" xlink:label="lab_ecd_PvpTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pay vs Performance Disclosure [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PvpTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PvpTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PvpTable" xlink:to="lab_ecd_PvpTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_019ce734-5c52-7cd1-a2cf-128a2aabcc90_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Liability, Statement of Financial Position [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:to="lab_us-gaap_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestReceivable_019ce734-5c52-71cc-b385-22646c9427d8_terseLabel_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_InterestReceivable_label_en-US" xlink:label="lab_us-gaap_InterestReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestReceivable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestReceivable" xlink:to="lab_us-gaap_InterestReceivable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_019ce734-5c52-72fa-a2f1-a8bf2e3fdf63_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsAbstract_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transactions [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsAbstract" xlink:to="lab_us-gaap_RelatedPartyTransactionsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_019ce734-5c52-7949-a247-ca1f978264a7_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash consideration paid to shareholders at Closing for fractional shares</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Cash Consideration Paid To Shareholders</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Cash Consideration Paid To Shareholders</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:href="kg-20260331.xsd#kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredCashConsiderationPaidToShareholders" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_019ce734-5ba0-7c9d-b4fe-6e9c30dcad73_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total equity securities subject to contractual sale restrictions</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:to="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_USTreasuryBondSecuritiesMember_019ce734-5cd9-7156-9a08-3c437ab6eabe_terseLabel_en-US" xlink:label="lab_us-gaap_USTreasuryBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. treasury bonds</link:label>
    <link:label id="lab_us-gaap_USTreasuryBondSecuritiesMember_label_en-US" xlink:label="lab_us-gaap_USTreasuryBondSecuritiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">US Treasury Bond Securities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_USTreasuryBondSecuritiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_USTreasuryBondSecuritiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_USTreasuryBondSecuritiesMember" xlink:to="lab_us-gaap_USTreasuryBondSecuritiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1_019ce734-5cd9-7431-8044-ee6e2455d8f9_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net paid losses related to Current year</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Claims Paid, Current Year</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:to="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseClaimsPaidCurrentYear1" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019ce734-5ba0-778a-af87-fda7395b9f57_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019ce734-5ba0-7fd7-91bf-7b5bc9d331e1_negatedLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_019ce734-5ba0-7653-99fc-4ac6470f263e_totalLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GainLossOnInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GainLossOnInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_GainLossOnInvestments" xlink:to="lab_us-gaap_GainLossOnInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ProFormaMember_019e039b-b97e-71bf-a0e1-c3ee0e474804_terseLabel_en-US" xlink:label="lab_srt_ProFormaMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pro Forma</link:label>
    <link:label id="lab_srt_ProFormaMember_label_en-US" xlink:label="lab_srt_ProFormaMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pro Forma [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProFormaMember" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProFormaMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProFormaMember" xlink:to="lab_srt_ProFormaMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_019ce734-5ba0-78fd-ac46-c5ce5a45f55d_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total before securities with single maturities, fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member_019d33da-9605-778f-a44b-223366d4d6f4_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 2</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 2 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_019ce734-5ba0-72e1-a90a-4bcdcccd09a0_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Funds withheld receivable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Receivable, Current</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:to="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_019ce734-5c52-726c-b470-924f6426b821_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, available-for-sale, at fair value, amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_019ce734-5c52-793f-b18d-d26b48a0c51f_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Original or amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:to="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_terseLabel_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:label id="lab_ecd_OtherPerfMeasureAmt_label_en-US" xlink:label="lab_ecd_OtherPerfMeasureAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Performance Measure, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_OtherPerfMeasureAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_OtherPerfMeasureAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_OtherPerfMeasureAmt" xlink:to="lab_ecd_OtherPerfMeasureAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_019d3d3d-27cb-7e42-936e-af7b70aab37c_verboseLabel_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Value of Business Acquired</link:label>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_019d3d39-fa85-7af1-b323-e29448950a15_terseLabel_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortization expense: VOBA</link:label>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_label_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Value of Business Acquired [Member]</link:label>
    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_documentation_en-US" xlink:label="lab_kg_ValueOfBusinessAcquiredMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Value of Business Acquired</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ValueOfBusinessAcquiredMember" xlink:href="kg-20260331.xsd#kg_ValueOfBusinessAcquiredMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ValueOfBusinessAcquiredMember" xlink:to="lab_kg_ValueOfBusinessAcquiredMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GLSToADCMember_019d3d06-b6b1-7be9-9c18-76ec852fe854_terseLabel_en-US" xlink:label="lab_kg_GLSToADCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GLS to ADC</link:label>
    <link:label id="lab_kg_GLSToADCMember_label_en-US" xlink:label="lab_kg_GLSToADCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GLS to ADC [Member]</link:label>
    <link:label id="lab_kg_GLSToADCMember_documentation_en-US" xlink:label="lab_kg_GLSToADCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GLS to ADC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GLSToADCMember" xlink:href="kg-20260331.xsd#kg_GLSToADCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GLSToADCMember" xlink:to="lab_kg_GLSToADCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_019ce734-5cd9-7aa4-8ca6-72c44dcce5f1_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyDomain" xlink:to="lab_us-gaap_RelatedPartyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BarryZyskindMember_019ce734-5c52-7e2e-9a0d-45dbb7e9a5e5_terseLabel_en-US" xlink:label="lab_kg_BarryZyskindMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Barry Zyskind</link:label>
    <link:label id="lab_kg_BarryZyskindMember_label_en-US" xlink:label="lab_kg_BarryZyskindMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Barry Zyskind [Member]</link:label>
    <link:label id="lab_kg_BarryZyskindMember_documentation_en-US" xlink:label="lab_kg_BarryZyskindMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Barry Zyskind</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BarryZyskindMember" xlink:href="kg-20260331.xsd#kg_BarryZyskindMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BarryZyskindMember" xlink:to="lab_kg_BarryZyskindMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_019d33da-9605-7481-a0bc-825e425050a9_terseLabel_en-US" xlink:label="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Duration matched discount rates</link:label>
    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_label_en-US" xlink:label="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Duration Matched Discount Rates [Member]</link:label>
    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_documentation_en-US" xlink:label="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Measurement Input, Duration Matched Discount Rates</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:href="kg-20260331.xsd#kg_MeasurementInputDurationMatchedDiscountRatesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:to="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_019ce734-5c52-76be-bed1-7c4ae0be34f2_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Measurements</link:label>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_label_en-US" xlink:label="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueOfFinancialInstrumentsPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:to="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_019ce734-5c52-748f-ac15-0186af4eccbf_terseLabel_en-US" xlink:label="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share Reinsurance Segment</link:label>
    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Quota Share Reinsurance Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:href="kg-20260331.xsd#kg_AmtrustQuotaShareReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:to="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsAbstract_019ce734-5cd9-7354-b706-7781d74bb078_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investments:</link:label>
    <link:label id="lab_us-gaap_InvestmentsAbstract_label_en-US" xlink:label="lab_us-gaap_InvestmentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentsAbstract" xlink:to="lab_us-gaap_InvestmentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityDomain_019ce734-5c52-72d9-b1a6-3cca5da24574_terseLabel_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:label id="lab_dei_EntityDomain_label_en-US" xlink:label="lab_dei_EntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityDomain" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityDomain" xlink:to="lab_dei_EntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_019ce734-5c52-7f8c-a735-adf69c86e200_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash provided by investing activities</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:to="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_terseLabel_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table</link:label>
    <link:label id="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember_label_en-US" xlink:label="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Change in Present Value of Accumulated Benefit for All Pension Plans Reported in Summary Compensation Table [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:to="lab_ecd_AggtChngPnsnValInSummryCompstnTblForAplblYrMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_019ce734-5ba0-7a86-b510-32fc735b3f8b_terseLabel_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:label id="lab_dei_DocumentFiscalYearFocus_label_en-US" xlink:label="lab_dei_DocumentFiscalYearFocus" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Fiscal Year Focus</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFiscalYearFocus" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFiscalYearFocus"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFiscalYearFocus" xlink:to="lab_dei_DocumentFiscalYearFocus" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_019ce734-5cd9-7df6-8d74-c6ee6c4b7244_terseLabel_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Effect of Ceded Reinsurance on Net Premiums Written and Earned and on Net Loss and LAE</link:label>
    <link:label id="lab_us-gaap_EffectsOfReinsuranceTableTextBlock_label_en-US" xlink:label="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effects of Reinsurance [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectsOfReinsuranceTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:to="lab_us-gaap_EffectsOfReinsuranceTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_019ce734-5c52-79ce-87e4-794b87de2633_terseLabel_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Presentation</link:label>
    <link:label id="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Basis of Accounting, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BasisOfAccountingPolicyPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:to="lab_us-gaap_BasisOfAccountingPolicyPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_019ce734-5c52-728f-8607-fbba2d5687a4_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, right-of-use asset</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseRightOfUseAsset_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Right-of-Use Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseRightOfUseAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseRightOfUseAsset" xlink:to="lab_us-gaap_OperatingLeaseRightOfUseAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfGainLossOnInvestmentsTable_019ce734-5c52-7631-b7b9-4e822f5c09c9_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfGainLossOnInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Gain (Loss) on Securities [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfGainLossOnInvestmentsTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfGainLossOnInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Gain (Loss) on Securities [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfGainLossOnInvestmentsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfGainLossOnInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfGainLossOnInvestmentsTable" xlink:to="lab_us-gaap_ScheduleOfGainLossOnInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfInsuranceCarriers_019ce734-5c52-7937-b429-2a60a70ac157_terseLabel_en-US" xlink:label="lab_kg_NumberOfInsuranceCarriers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of insurance carriers</link:label>
    <link:label id="lab_kg_NumberOfInsuranceCarriers_label_en-US" xlink:label="lab_kg_NumberOfInsuranceCarriers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number of Insurance Carriers</link:label>
    <link:label id="lab_kg_NumberOfInsuranceCarriers_documentation_en-US" xlink:label="lab_kg_NumberOfInsuranceCarriers" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number of Insurance Carriers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfInsuranceCarriers" xlink:href="kg-20260331.xsd#kg_NumberOfInsuranceCarriers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfInsuranceCarriers" xlink:to="lab_kg_NumberOfInsuranceCarriers" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameDomain_019ce734-5cd9-7309-9239-695a768859b8_terseLabel_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:label id="lab_us-gaap_PlanNameDomain_label_en-US" xlink:label="lab_us-gaap_PlanNameDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Plan Name [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PlanNameDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PlanNameDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PlanNameDomain" xlink:to="lab_us-gaap_PlanNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_019ce734-5c52-7754-b316-4a12e4026732_terseLabel_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Principal Amount</link:label>
    <link:label id="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember_label_en-US" xlink:label="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reported Value Measurement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CarryingReportedAmountFairValueDisclosureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:to="lab_us-gaap_CarryingReportedAmountFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_OtherInvestmentsPercentOfTotal_019ce734-5c52-76e7-8197-73b1c1dd5d35_terseLabel_en-US" xlink:label="lab_kg_OtherInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total</link:label>
    <link:label id="lab_kg_OtherInvestmentsPercentOfTotal_label_en-US" xlink:label="lab_kg_OtherInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Investments, Percent of Total</link:label>
    <link:label id="lab_kg_OtherInvestmentsPercentOfTotal_documentation_en-US" xlink:label="lab_kg_OtherInvestmentsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Investments, Percent of Total</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherInvestmentsPercentOfTotal" xlink:href="kg-20260331.xsd#kg_OtherInvestmentsPercentOfTotal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherInvestmentsPercentOfTotal" xlink:to="lab_kg_OtherInvestmentsPercentOfTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent_019ce734-5cd9-78ef-95ea-89f406e3087b_terseLabel_en-US" xlink:label="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in net unrealized investment losses</link:label>
    <link:label id="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent_019ce734-5cd9-7921-8e82-11f2a4f6ed3d_verboseLabel_en-US" xlink:label="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Change, net of deferred income tax</link:label>
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    <link:label id="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent_documentation_en-US" xlink:label="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Investments Adjustment, Net of Tax, Portion Attributable To Parent</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfAccumulatedOtherComprehensiveIncomeLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic_019ce734-5ba0-7db5-8586-e73b51f2b86b_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss available to Kestrel common shareholders before discontinued operations, basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) from Continuing Operations Available to Common Shareholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossFromContinuingOperationsAvailableToCommonShareholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_019ce734-5ba1-7404-b3b4-923f6cb37904_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), before Tax [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossBeforeTaxPeriodIncreaseDecreaseAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetPurchaseAgreementMember_019ce734-5c52-7d70-a7ed-40e6a8be1e21_terseLabel_en-US" xlink:label="lab_kg_AssetPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Purchase Agreement</link:label>
    <link:label id="lab_kg_AssetPurchaseAgreementMember_label_en-US" xlink:label="lab_kg_AssetPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Purchase Agreement [Member]</link:label>
    <link:label id="lab_kg_AssetPurchaseAgreementMember_documentation_en-US" xlink:label="lab_kg_AssetPurchaseAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Purchase Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetPurchaseAgreementMember" xlink:href="kg-20260331.xsd#kg_AssetPurchaseAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetPurchaseAgreementMember" xlink:to="lab_kg_AssetPurchaseAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InsuranceLiabilitiesNet_019ce734-5c52-7faf-807e-0ee1faf8feee_terseLabel_en-US" xlink:label="lab_kg_InsuranceLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Insurance liabilities net</link:label>
    <link:label id="lab_kg_InsuranceLiabilitiesNet_label_en-US" xlink:label="lab_kg_InsuranceLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Liabilities Net</link:label>
    <link:label id="lab_kg_InsuranceLiabilitiesNet_documentation_en-US" xlink:label="lab_kg_InsuranceLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Insurance Liabilities Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InsuranceLiabilitiesNet" xlink:href="kg-20260331.xsd#kg_InsuranceLiabilitiesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InsuranceLiabilitiesNet" xlink:to="lab_kg_InsuranceLiabilitiesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DirectPremiumsWritten_019ce734-5c52-768d-a8df-572fe4e0d1c1_terseLabel_en-US" xlink:label="lab_us-gaap_DirectPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Direct</link:label>
    <link:label id="lab_us-gaap_DirectPremiumsWritten_label_en-US" xlink:label="lab_us-gaap_DirectPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Direct Premiums Written</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DirectPremiumsWritten" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DirectPremiumsWritten"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DirectPremiumsWritten" xlink:to="lab_us-gaap_DirectPremiumsWritten" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LPTADCAgreementMember_019ce734-5c52-7f8d-8c4f-5754de50757b_terseLabel_en-US" xlink:label="lab_kg_LPTADCAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">LPT/ADC Agreement</link:label>
    <link:label id="lab_kg_LPTADCAgreementMember_label_en-US" xlink:label="lab_kg_LPTADCAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">LPT/ADC Agreement [Member]</link:label>
    <link:label id="lab_kg_LPTADCAgreementMember_documentation_en-US" xlink:label="lab_kg_LPTADCAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">LPT/ADC Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LPTADCAgreementMember" xlink:href="kg-20260331.xsd#kg_LPTADCAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LPTADCAgreementMember" xlink:to="lab_kg_LPTADCAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_019ce734-5c52-7844-b760-340f088cfc78_verboseLabel_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_019ce734-5c52-760c-ab6a-3d93464ee61b_terseLabel_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance legacy business</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_label_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance Segment [Member]</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Reinsurance Segment [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustReinsuranceSegmentMember" xlink:href="kg-20260331.xsd#kg_AmTrustReinsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustReinsuranceSegmentMember" xlink:to="lab_kg_AmTrustReinsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrDuration_terseLabel_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Arrangement Duration</link:label>
    <link:label id="lab_ecd_TrdArrDuration_label_en-US" xlink:label="lab_ecd_TrdArrDuration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Duration</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrDuration" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrDuration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrDuration" xlink:to="lab_ecd_TrdArrDuration" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock_019ce734-5ba0-7172-9e08-aa8663908ee6_terseLabel_en-US" xlink:label="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Cost and Fair Values of the Equity Securities and Privately Held Securities Held Subject to Contractual Sale Restrictions</link:label>
    <link:label id="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock_label_en-US" xlink:label="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Trading, and Equity Securities, FV-NI [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:to="lab_us-gaap_TradingSecuritiesAndCertainTradingAssetsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_019ce734-5cd9-7184-aabd-0ea229fd15f3_terseLabel_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:label id="lab_us-gaap_StatementBusinessSegmentsAxis_label_en-US" xlink:label="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementBusinessSegmentsAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementBusinessSegmentsAxis" xlink:to="lab_us-gaap_StatementBusinessSegmentsAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MaidenReinsuranceMember_019ce734-5cd9-72b9-90ee-4227417135fb_terseLabel_en-US" xlink:label="lab_kg_MaidenReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maiden Reinsurance</link:label>
    <link:label id="lab_kg_MaidenReinsuranceMember_label_en-US" xlink:label="lab_kg_MaidenReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maiden Reinsurance [Member]</link:label>
    <link:label id="lab_kg_MaidenReinsuranceMember_documentation_en-US" xlink:label="lab_kg_MaidenReinsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maiden Reinsurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenReinsuranceMember" xlink:href="kg-20260331.xsd#kg_MaidenReinsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MaidenReinsuranceMember" xlink:to="lab_kg_MaidenReinsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_LocalPhoneNumber_019ce734-5cd9-77c2-bbdf-137c1d478994_terseLabel_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:label id="lab_dei_LocalPhoneNumber_label_en-US" xlink:label="lab_dei_LocalPhoneNumber" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Local Phone Number</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_LocalPhoneNumber" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_LocalPhoneNumber"/>
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    <link:label id="lab_kg_UnderwritingIncomeLossNet_019ce734-5ba0-7489-b004-374e79363399_totalLabel_en-US" xlink:label="lab_kg_UnderwritingIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Underwriting loss and fee income</link:label>
    <link:label id="lab_kg_UnderwritingIncomeLossNet_label_en-US" xlink:label="lab_kg_UnderwritingIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underwriting Income Loss Net</link:label>
    <link:label id="lab_kg_UnderwritingIncomeLossNet_documentation_en-US" xlink:label="lab_kg_UnderwritingIncomeLossNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Net premiums earned less: net losses and loss expenses, acquisition costs and general and administrative expenses directly related to underwriting activities.</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_UnderwritingIncomeLossNet" xlink:href="kg-20260331.xsd#kg_UnderwritingIncomeLossNet"/>
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    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_terseLabel_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure</link:label>
    <link:label id="lab_ecd_Additional402vDisclosureTextBlock_label_en-US" xlink:label="lab_ecd_Additional402vDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Additional 402(v) Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Additional402vDisclosureTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Additional402vDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Additional402vDisclosureTextBlock" xlink:to="lab_ecd_Additional402vDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember_019ce734-5c52-7680-aa78-b308805875b1_terseLabel_en-US" xlink:label="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
    <link:label id="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember_label_en-US" xlink:label="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ArrangementsAndNonarrangementTransactionsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:to="lab_us-gaap_ArrangementsAndNonarrangementTransactionsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff_019ce734-5cd9-7bcd-8c0a-8311e8d8cbde_terseLabel_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Write off on the accrued interest receivable</link:label>
    <link:label id="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff_label_en-US" xlink:label="lab_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financing Receivable, Accrued Interest, Writeoff</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FinancingReceivableAccruedInterestWriteoff" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FinancingReceivableAccruedInterestWriteoff"/>
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    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_019ce734-5c52-73df-8f7f-ac64ccb012ed_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Others, net</link:label>
    <link:label id="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities_label_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payment for (Proceeds from) Other Investing Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForProceedsFromOtherInvestingActivities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForProceedsFromOtherInvestingActivities"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_019ce734-5c52-78a0-b32e-c67428407e6c_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intangible assets</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedIntangibleAssetsOtherThanGoodwill" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Recognized Asset Acquired, Identifiable Intangible Asset, Excluding Goodwill</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCashAndEquivalents"/>
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    <link:label id="lab_us-gaap_AssetsAbstract_019ce734-5c52-7bc0-abbc-186d53aa4976_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ASSETS</link:label>
    <link:label id="lab_us-gaap_AssetsAbstract_label_en-US" xlink:label="lab_us-gaap_AssetsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsAbstract" xlink:to="lab_us-gaap_AssetsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_019ce734-5ba0-7762-836e-12034add141f_terseLabel_en-US" xlink:label="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Minimum Excess Funding Requirement</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_label_en-US" xlink:label="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Minimum Excess Funding Requirement [Member]</link:label>
    <link:label id="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_documentation_en-US" xlink:label="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Post-Termination Endorsement, Minimum Excess Funding Requirement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:href="kg-20260331.xsd#kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:to="lab_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_terseLabel_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change</link:label>
    <link:label id="lab_ecd_UndrlygSecurityMktPriceChngPct_label_en-US" xlink:label="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Underlying Security Market Price Change, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_UndrlygSecurityMktPriceChngPct"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_UndrlygSecurityMktPriceChngPct" xlink:to="lab_ecd_UndrlygSecurityMktPriceChngPct" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_019ce734-5ba0-73d4-8835-40038e5e839f_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentAxis_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentAxis" xlink:to="lab_us-gaap_DebtInstrumentAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_019ce734-5c52-7440-961d-c6306c621e2c_terseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_019ce734-5c52-7a89-b3d6-eb8ef4395686_verboseLabel_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loan receivable from related party</link:label>
    <link:label id="lab_us-gaap_LoansAndLeasesReceivableRelatedParties_label_en-US" xlink:label="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loans and Leases Receivable, Related Parties</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LoansAndLeasesReceivableRelatedParties"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:to="lab_us-gaap_LoansAndLeasesReceivableRelatedParties" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_019ce734-5cd9-73de-8f1e-3545c4d6b868_negatedLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">12 Months or More</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_019ce734-5c52-7b35-a7ff-24740cddf453_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value of Financial Instruments</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresTextBlock" xlink:to="lab_us-gaap_FairValueDisclosuresTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_019ce734-5cd9-72b4-bac7-62e999560bd5_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionLineItems_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionLineItems" xlink:to="lab_us-gaap_BusinessAcquisitionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_019ce734-5ba0-7269-a987-999326cff0b6_terseLabel_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative arrangement, reserves expected to be commuted, exit cost</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_label_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted, Exit Cost</link:label>
    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_documentation_en-US" xlink:label="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement, Reserves Expected to be Commuted, Exit Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:href="kg-20260331.xsd#kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:to="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_019dbb16-4484-7057-a491-3118b20d7e42_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares repurchased</link:label>
    <link:label id="lab_us-gaap_TreasuryStockValueAcquiredCostMethod_label_en-US" xlink:label="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Value, Acquired, Cost Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockValueAcquiredCostMethod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:to="lab_us-gaap_TreasuryStockValueAcquiredCostMethod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019ce734-5c52-78cd-a57c-68b8b21c1896_verboseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Stated interest rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_019ce734-5c52-76cb-8c85-71c7147181fb_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Coupon rate</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Interest Rate, Stated Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentInterestRateStatedPercentage"/>
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    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_019ce734-5c52-7c0b-a0d7-1cea83bf5658_terseLabel_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_label_en-US" xlink:label="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Name [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis"/>
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    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_019ce734-5c52-7ac7-864f-659fb7e28d10_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Premiums by Major Line of Business</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from External Customers by Products and Services [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock"/>
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    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_019ce734-5c52-7c1b-90b6-69cdd493755b_terseLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Less than 12 Months</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than Twelve Months, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than Twelve Months, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue"/>
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    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_019ce734-5ba0-701e-b470-1ee37a951c9d_terseLabel_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Axis]</link:label>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_label_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Axis]</link:label>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_documentation_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EntitiesOwnedByRelatedPartiesAxis" xlink:href="kg-20260331.xsd#kg_EntitiesOwnedByRelatedPartiesAxis"/>
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    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_019ce734-5cd9-7791-b2cb-b2c83f2d688e_terseLabel_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other non-cash expenses (credit losses, depreciation, amortization, leases)</link:label>
    <link:label id="lab_us-gaap_DepreciationAmortizationAndAccretionNet_label_en-US" xlink:label="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Depreciation, Amortization and Accretion, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DepreciationAmortizationAndAccretionNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:to="lab_us-gaap_DepreciationAmortizationAndAccretionNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityRegistrantName_019ce734-5c52-70d7-aba9-13348d168e78_terseLabel_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:label id="lab_dei_EntityRegistrantName_label_en-US" xlink:label="lab_dei_EntityRegistrantName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Registrant Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityRegistrantName" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityRegistrantName" xlink:to="lab_dei_EntityRegistrantName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_terseLabel_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method</link:label>
    <link:label id="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock_label_en-US" xlink:label="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Price or TSR Estimation Method [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_StkPrcOrTsrEstimationMethodTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:to="lab_ecd_StkPrcOrTsrEstimationMethodTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessAcquisitionOptionTerm_019ce734-5ba0-7921-b53b-16819efb0444_terseLabel_en-US" xlink:label="lab_kg_BusinessAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquire option term</link:label>
    <link:label id="lab_kg_BusinessAcquisitionOptionTerm_label_en-US" xlink:label="lab_kg_BusinessAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Acquisition, Option Term</link:label>
    <link:label id="lab_kg_BusinessAcquisitionOptionTerm_documentation_en-US" xlink:label="lab_kg_BusinessAcquisitionOptionTerm" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Acquisition, Option Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessAcquisitionOptionTerm" xlink:href="kg-20260331.xsd#kg_BusinessAcquisitionOptionTerm"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessAcquisitionOptionTerm" xlink:to="lab_kg_BusinessAcquisitionOptionTerm" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustLegacySegmentMember_019ce734-5ba0-759d-99fd-d59de4d26d56_verboseLabel_en-US" xlink:label="lab_kg_AmTrustLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Legacy Reinsurance</link:label>
    <link:label id="lab_kg_AmTrustLegacySegmentMember_label_en-US" xlink:label="lab_kg_AmTrustLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust Legacy Segment [Member]</link:label>
    <link:label id="lab_kg_AmTrustLegacySegmentMember_documentation_en-US" xlink:label="lab_kg_AmTrustLegacySegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust Legacy Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustLegacySegmentMember" xlink:href="kg-20260331.xsd#kg_AmTrustLegacySegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustLegacySegmentMember" xlink:to="lab_kg_AmTrustLegacySegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_019ce734-5c52-7fe5-9360-987480ba71df_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liabilities held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_019ce734-5c52-74f4-9d36-e5b8e6b40775_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Liabilities held for sale</link:label>
    <link:label id="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation_label_en-US" xlink:label="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:to="lab_us-gaap_LiabilitiesOfDisposalGroupIncludingDiscontinuedOperation" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AlternativeInvestmentMeasurementInput_019d33da-9605-75e1-8401-227480d9973b_terseLabel_en-US" xlink:label="lab_us-gaap_AlternativeInvestmentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Investments, measurement inputs</link:label>
    <link:label id="lab_us-gaap_AlternativeInvestmentMeasurementInput_label_en-US" xlink:label="lab_us-gaap_AlternativeInvestmentMeasurementInput" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alternative Investment, Measurement Input</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestmentMeasurementInput" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AlternativeInvestmentMeasurementInput"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AlternativeInvestmentMeasurementInput" xlink:to="lab_us-gaap_AlternativeInvestmentMeasurementInput" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_019ce734-5c52-7891-be31-e4c4e9f7af86_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Future premiums and losses related to policies, percentage</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Future Premiums and Losses Related to Policies</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Future Premiums and Losses Related to Policies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:to="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019ce734-5c52-7682-b38a-4e646b3ac20e_totalLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total investments</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_019ce734-5c52-7810-be97-534f0e0f2ca8_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial instruments, fair value</link:label>
    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_label_en-US" xlink:label="lab_us-gaap_AssetsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets, Fair Value Disclosure</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsFairValueDisclosure" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsFairValueDisclosure"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsFairValueDisclosure" xlink:to="lab_us-gaap_AssetsFairValueDisclosure" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_019ce734-5c52-70b2-9e2e-f5e2390550b9_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percent basis currency equivalent of maximum limit of liability attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Basis Currency Equivalent of Maximum Limit of Liability Attaching</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Basis Currency Equivalent of Maximum Limit of Liability Attaching</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:to="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock_019ce734-5c52-7e43-8075-1548e6681c5b_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Allowance for Expected Credit Losses on Reinsurance Recoverable</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Allowance for Credit Loss [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:to="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_019ce734-5c52-720e-9b2c-8346fd96fb7f_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party [Axis]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related and Nonrelated Parties [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionsByRelatedPartyAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:to="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyLineItems_019ce734-5cd9-7191-a7cf-eff7c656674a_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance Retention Policy [Line Items]</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRetentionPolicyLineItems_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRetentionPolicyLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Retention [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRetentionPolicyLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRetentionPolicyLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceRetentionPolicyLineItems" xlink:to="lab_us-gaap_ReinsuranceRetentionPolicyLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_019ce734-5ba0-71f4-b2f4-467ddfcc4ae6_totalLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net cash used in continuing operations</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Continuing Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:to="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_TypeOfArrangementAxis_019ce734-5c52-7a55-b742-1ed66fd41612_terseLabel_en-US" xlink:label="lab_us-gaap_TypeOfArrangementAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
    <link:label id="lab_us-gaap_TypeOfArrangementAxis_label_en-US" xlink:label="lab_us-gaap_TypeOfArrangementAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TypeOfArrangementAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TypeOfArrangementAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_TypeOfArrangementAxis" xlink:to="lab_us-gaap_TypeOfArrangementAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_RestatementDateAxis_terseLabel_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restatement Determination Date:</link:label>
    <link:label id="lab_ecd_RestatementDateAxis_label_en-US" xlink:label="lab_ecd_RestatementDateAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restatement Determination Date [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_RestatementDateAxis" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_RestatementDateAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_RestatementDateAxis" xlink:to="lab_ecd_RestatementDateAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ControllingInterestOwnershipPercentage_019ce734-5c52-7da9-8920-a555dd6f1a27_terseLabel_en-US" xlink:label="lab_kg_ControllingInterestOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Controlling interest, ownership percentage</link:label>
    <link:label id="lab_kg_ControllingInterestOwnershipPercentage_label_en-US" xlink:label="lab_kg_ControllingInterestOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Controlling Interest, Ownership Percentage</link:label>
    <link:label id="lab_kg_ControllingInterestOwnershipPercentage_documentation_en-US" xlink:label="lab_kg_ControllingInterestOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Controlling Interest, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ControllingInterestOwnershipPercentage" xlink:href="kg-20260331.xsd#kg_ControllingInterestOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ControllingInterestOwnershipPercentage" xlink:to="lab_kg_ControllingInterestOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_019ce734-5cd9-7d02-98cd-92914297da9a_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Intercompany settlement</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_label_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Intercompany Settlement</link:label>
    <link:label id="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_documentation_en-US" xlink:label="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Intercompany Settlement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:href="kg-20260331.xsd#kg_BusinessCombinationConsiderationTransferredIntercompanySettlement"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:to="lab_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_019ce734-5c52-7351-a635-da0043628ea8_terseLabel_en-US" xlink:label="lab_kg_AmTrustNorthAmericaIncMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust North America Inc</link:label>
    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_label_en-US" xlink:label="lab_kg_AmTrustNorthAmericaIncMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust North America Inc [Member]</link:label>
    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_documentation_en-US" xlink:label="lab_kg_AmTrustNorthAmericaIncMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust North America Inc</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmTrustNorthAmericaIncMember" xlink:href="kg-20260331.xsd#kg_AmTrustNorthAmericaIncMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmTrustNorthAmericaIncMember" xlink:to="lab_kg_AmTrustNorthAmericaIncMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_019ce734-5ba1-77aa-8e7f-13837acc5628_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss) [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:to="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member_019d33da-9605-724c-9247-2487346dc202_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investments - preferred shares 4</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 4 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 4</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_019ce734-5c52-7c7e-b1c9-eab4ae19ca34_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued interest on collateral held by related party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Accrued Interest on Collateral Held by Related Party</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Accrued Interest on Collateral Held by Related Party</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_019ce734-5c52-7303-b5fb-f7dc3602b87c_terseLabel_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest and amortization expenses</link:label>
    <link:label id="lab_us-gaap_InterestExpenseDebt_label_en-US" xlink:label="lab_us-gaap_InterestExpenseDebt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Expense, Debt</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestExpenseDebt" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestExpenseDebt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestExpenseDebt" xlink:to="lab_us-gaap_InterestExpenseDebt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedInvestments_019ce734-5c52-7cea-8f2e-fad7b309e3ac_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted investments</link:label>
    <link:label id="lab_us-gaap_RestrictedInvestments_label_en-US" xlink:label="lab_us-gaap_RestrictedInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedInvestments" xlink:to="lab_us-gaap_RestrictedInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_019ce734-5c52-705f-82c7-b8f71f8041c4_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting, Revenue Reconciling Item [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting, Revenue Reconciling Item [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingRevenueReconcilingItemLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:to="lab_us-gaap_SegmentReportingRevenueReconcilingItemLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrIndName_terseLabel_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_TrdArrIndName_label_en-US" xlink:label="lab_ecd_TrdArrIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrIndName" xlink:to="lab_ecd_TrdArrIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_019ce734-5ba0-771b-8891-7906a029bb9e_terseLabel_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of Revenue from Segments to Consolidated [Table]</link:label>
    <link:label id="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable_label_en-US" xlink:label="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation of Revenue from Segments to Consolidated [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:to="lab_us-gaap_ReconciliationOfRevenueFromSegmentsToConsolidatedTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_019ce734-5cd9-7f4c-91c3-9b1b0e7624d8_negatedLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Less than 12 Months</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthan12MonthsAccumulatedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LeahKarfunkelMember_019ce734-5cd9-7ef7-a1bc-b4d1077090ad_terseLabel_en-US" xlink:label="lab_kg_LeahKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leah Karfunkel</link:label>
    <link:label id="lab_kg_LeahKarfunkelMember_label_en-US" xlink:label="lab_kg_LeahKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leah Karfunkel [Member]</link:label>
    <link:label id="lab_kg_LeahKarfunkelMember_documentation_en-US" xlink:label="lab_kg_LeahKarfunkelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Leah Karfunkel</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LeahKarfunkelMember" xlink:href="kg-20260331.xsd#kg_LeahKarfunkelMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LeahKarfunkelMember" xlink:to="lab_kg_LeahKarfunkelMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_019ce734-5c52-74c3-818f-01ee30cbfc54_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt instrument, principal amount</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentFaceAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentFaceAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Face Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentFaceAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentFaceAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentFaceAmount" xlink:to="lab_us-gaap_DebtInstrumentFaceAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_019ce734-5ba0-749c-9a88-15f54a29bd0d_terseLabel_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:label id="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_label_en-US" xlink:label="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Comprehensive Income [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:to="lab_us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_019ce734-5ba1-7a74-bca6-257de8878439_totalLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net equity portion of consideration transferred at Closing</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Consideration Transferred, Equity Interest</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:to="lab_us-gaap_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_019ce734-5c52-73f7-a90d-ce440f8c2a4c_terseLabel_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:label id="lab_srt_ShareRepurchaseProgramAxis_label_en-US" xlink:label="lab_srt_ShareRepurchaseProgramAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share Repurchase Program [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ShareRepurchaseProgramAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ShareRepurchaseProgramAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ShareRepurchaseProgramAxis" xlink:to="lab_srt_ShareRepurchaseProgramAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PreferredStockMember_019ce734-5c52-72f5-9d57-9649af63cb42_terseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Privately held preferred stocks</link:label>
    <link:label id="lab_us-gaap_PreferredStockMember_label_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Preferred Stock [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PreferredStockMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PreferredStockMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PreferredStockMember" xlink:to="lab_us-gaap_PreferredStockMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_terseLabel_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_AwardsCloseToMnpiDiscIndName_label_en-US" xlink:label="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Awards Close in Time to MNPI Disclosures, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardsCloseToMnpiDiscIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardsCloseToMnpiDiscIndName" xlink:to="lab_ecd_AwardsCloseToMnpiDiscIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_019ce734-5c52-781a-ab54-00df9a05ce45_negatedLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Unearned premiums</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Unearned Premiums</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Unearned Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined</link:label>
    <link:label id="lab_ecd_AggtErrCompNotYetDeterminedTextBlock_label_en-US" xlink:label="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Aggregate Erroneous Compensation Not Yet Determined [Text Block]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:to="lab_ecd_AggtErrCompNotYetDeterminedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherCommitment_019ce734-5c52-7b40-b056-2c5fff7348c8_terseLabel_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Guarantees provided to lenders on behalf of real estate joint venture</link:label>
    <link:label id="lab_us-gaap_OtherCommitment_label_en-US" xlink:label="lab_us-gaap_OtherCommitment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Commitment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherCommitment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherCommitment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherCommitment" xlink:to="lab_us-gaap_OtherCommitment" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesDomain_019ce734-5ba0-751c-a95f-2e4ab2027fce_terseLabel_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Domain]</link:label>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesDomain_label_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Domain]</link:label>
    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesDomain_documentation_en-US" xlink:label="lab_kg_EntitiesOwnedByRelatedPartiesDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Entities Owned by Related Parties [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EntitiesOwnedByRelatedPartiesDomain" xlink:href="kg-20260331.xsd#kg_EntitiesOwnedByRelatedPartiesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EntitiesOwnedByRelatedPartiesDomain" xlink:to="lab_kg_EntitiesOwnedByRelatedPartiesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities_019ce734-5ba0-76e0-9603-cacc99a04f57_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, at fair value</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Equity Securities</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed, Equity Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AlternativeInvestment_019ce734-5ba1-7d94-9296-c59cc273fa4d_terseLabel_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other investments</link:label>
    <link:label id="lab_us-gaap_AlternativeInvestment_label_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Alternative Investment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AlternativeInvestment" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AlternativeInvestment"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AlternativeInvestment" xlink:to="lab_us-gaap_AlternativeInvestment" xlink:type="arc" order="1"/>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Restricted Cash and Cash Equivalents</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Business Combination Recognized Identifiable Assets Acquired And Liabilities Assumed Restricted Cash and Cash Equivalents</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents" xlink:href="kg-20260331.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_019ce734-5c52-7350-870f-ec5221ca67d1_verboseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Share-based compensation expense</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue"/>
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    <link:label id="lab_srt_LitigationCaseAxis_019d3d06-b6b1-7539-b4a6-b210d460b760_terseLabel_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:label id="lab_srt_LitigationCaseAxis_label_en-US" xlink:label="lab_srt_LitigationCaseAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Litigation Case [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_LitigationCaseAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_LitigationCaseAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_LitigationCaseAxis" xlink:to="lab_srt_LitigationCaseAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentDomain_019ce734-5ba1-7213-a730-5e07f6a20d0f_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_019ce734-5ba1-7e0e-839f-f19ee7ff4dc0_verboseLabel_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:label id="lab_us-gaap_SegmentDomain_label_en-US" xlink:label="lab_us-gaap_SegmentDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentDomain" xlink:to="lab_us-gaap_SegmentDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_019ddf7f-97a7-7f10-b151-e89f1646e3f5_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementLocationAxis_label_en-US" xlink:label="lab_us-gaap_IncomeStatementLocationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement of Income Location, Balance [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementLocationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementLocationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementLocationAxis" xlink:to="lab_us-gaap_IncomeStatementLocationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_A2025EquityIncentivePlanMember_019ce734-5ba1-7ede-a07b-adb996e7f3fe_terseLabel_en-US" xlink:label="lab_kg_A2025EquityIncentivePlanMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025 Equity Incentive Plan</link:label>
    <link:label id="lab_kg_A2025EquityIncentivePlanMember_label_en-US" xlink:label="lab_kg_A2025EquityIncentivePlanMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">2025 Equity Incentive Plan [Member]</link:label>
    <link:label id="lab_kg_A2025EquityIncentivePlanMember_documentation_en-US" xlink:label="lab_kg_A2025EquityIncentivePlanMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">2025 Equity Incentive Plan</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_A2025EquityIncentivePlanMember" xlink:href="kg-20260331.xsd#kg_A2025EquityIncentivePlanMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_A2025EquityIncentivePlanMember" xlink:to="lab_kg_A2025EquityIncentivePlanMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedMaturitiesMember_019ce734-5ba1-76ae-8407-e3d63b0558c5_verboseLabel_en-US" xlink:label="lab_us-gaap_FixedMaturitiesMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities</link:label>
    <link:label id="lab_us-gaap_FixedMaturitiesMember_label_en-US" xlink:label="lab_us-gaap_FixedMaturitiesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FixedMaturitiesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FixedMaturitiesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FixedMaturitiesMember" xlink:to="lab_us-gaap_FixedMaturitiesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_019ce734-5ba0-7c3d-8eee-5fc6b686f083_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value, Measurements, Fair Value Hierarchy [Domain]</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Hierarchy and NAV [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementsFairValueHierarchyDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:to="lab_us-gaap_FairValueMeasurementsFairValueHierarchyDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockOwnershipAxis_019df410-7564-77fb-80ec-a39373f86a81_terseLabel_en-US" xlink:label="lab_kg_CommonStockOwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Axis]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipAxis_label_en-US" xlink:label="lab_kg_CommonStockOwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock Ownership [Axis]</link:label>
    <link:label id="lab_kg_CommonStockOwnershipAxis_documentation_en-US" xlink:label="lab_kg_CommonStockOwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock Ownership</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommonStockOwnershipAxis" xlink:href="kg-20260331.xsd#kg_CommonStockOwnershipAxis"/>
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    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_019ce734-5c52-7734-bfe1-fc14f2c00358_terseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Change in net unrealized gains on investment</link:label>
    <link:label id="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember_label_en-US" xlink:label="lab_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AOCI, Accumulated Gain (Loss), Debt Securities, Available-for-Sale, Parent [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedNetUnrealizedInvestmentGainLossMember"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable_019ce734-5c52-76a8-b5d5-faf688ed1593_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Reinsurance balances receivable, net</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Premiums Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInPremiumsReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInPremiumsReceivable"/>
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    <link:label id="lab_us-gaap_SeniorNotesMember_019ce734-5cd9-7e29-8478-063cb54006dd_terseLabel_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Senior Notes</link:label>
    <link:label id="lab_us-gaap_SeniorNotesMember_label_en-US" xlink:label="lab_us-gaap_SeniorNotesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SeniorNotesMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SeniorNotesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SeniorNotesMember" xlink:to="lab_us-gaap_SeniorNotesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_019ce734-5cd9-7a95-8127-f8971269f382_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage ceded</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceded Business Amount</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Percent Of Ceded Business Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfCededBusinessAmount" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionPercentOfCededBusinessAmount"/>
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    <link:label id="lab_kg_NotesReceivableRelatedPartyMember_label_en-US" xlink:label="lab_kg_NotesReceivableRelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Notes Receivable, Related Party [Member]</link:label>
    <link:label id="lab_kg_NotesReceivableRelatedPartyMember_documentation_en-US" xlink:label="lab_kg_NotesReceivableRelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Notes Receivable, Related Party [Member]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NotesReceivableRelatedPartyMember" xlink:to="lab_kg_NotesReceivableRelatedPartyMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_terseLabel_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Executive Categories</link:label>
    <link:label id="lab_ecd_AllExecutiveCategoriesMember_label_en-US" xlink:label="lab_ecd_AllExecutiveCategoriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Executive Categories [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllExecutiveCategoriesMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllExecutiveCategoriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllExecutiveCategoriesMember" xlink:to="lab_ecd_AllExecutiveCategoriesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense_019ce734-5c52-7a05-ae12-c1ed0110362c_verboseLabel_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net incurred losses related to Current year</link:label>
    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Year Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:to="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersCurrentYearClaimsAndClaimsAdjustmentExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019ce734-5c52-7122-a768-1e170bf27391_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission and other acquisition expenses</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019ce734-5c52-7454-8d0f-e783839c6a9b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Commission and other acquisition expenses</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_019ce734-5c52-78c6-b421-606eb0cba047_negatedLabel_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Commission and other acquisition expenses</link:label>
    <link:label id="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense_label_en-US" xlink:label="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Policy Acquisition Costs, Amortization Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:to="lab_us-gaap_DeferredPolicyAcquisitionCostAmortizationExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockValue_019ce734-5c52-7e01-8986-fa19ae45b23a_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares ($0.01 par value; 2026: 10,108,600 and 2025: 9,979,477 shares issued; 2026: 7,824,030 and 2025: 7,741,943 shares outstanding)</link:label>
    <link:label id="lab_us-gaap_CommonStockValue_label_en-US" xlink:label="lab_us-gaap_CommonStockValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Value, Issued</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockValue" xlink:to="lab_us-gaap_CommonStockValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_019ce734-5c52-73d0-97c5-81e190988016_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amount allocated to participating common shareholders, basic</link:label>
    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic_label_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Undistributed Earnings (Loss) Allocated to Participating Securities, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:to="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019ce734-5c52-7d53-b1ac-f9e68a6d4dd8_totalLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net premiums earned</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019ce734-5c52-7c7d-88ff-1ba42f6d06b2_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net premiums earned</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_019ce734-5c52-7acd-b370-e99c413adf2f_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net premiums earned</link:label>
    <link:label id="lab_us-gaap_PremiumsEarnedNet_label_en-US" xlink:label="lab_us-gaap_PremiumsEarnedNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PremiumsEarnedNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PremiumsEarnedNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PremiumsEarnedNet" xlink:to="lab_us-gaap_PremiumsEarnedNet" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_019ce734-5c52-7b2f-b73b-39818f9665ee_negatedLabel_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Other investments, gross losses</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_label_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Loss</link:label>
    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_documentation_en-US" xlink:label="lab_kg_MarketableSecuritiesRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Marketable Securities, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MarketableSecuritiesRealizedLoss" xlink:href="kg-20260331.xsd#kg_MarketableSecuritiesRealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MarketableSecuritiesRealizedLoss" xlink:to="lab_kg_MarketableSecuritiesRealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_019ce734-5ba0-72c2-80c4-7a6d49d62309_terseLabel_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:label id="lab_us-gaap_CommitmentsAndContingencies_label_en-US" xlink:label="lab_us-gaap_CommitmentsAndContingencies" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commitments and Contingencies</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommitmentsAndContingencies" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommitmentsAndContingencies"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommitmentsAndContingencies" xlink:to="lab_us-gaap_CommitmentsAndContingencies" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_019ce734-5c52-7274-ae9a-8a11fa82bcd4_terseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changes in liabilities &#8211; increase (decrease):</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Operating Liabilities [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:to="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_019ce734-5cd9-79fd-9a7e-00d52e791c91_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Based on NAV Practical Expedient</link:label>
    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_label_en-US" xlink:label="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Measured at Net Asset Value Per Share [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:to="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue_019ce734-5c52-77c5-a7ca-edff79a10a55_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net present value of total distributions</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Distributions, Net Present Value</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Distributions, Net Present Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:href="kg-20260331.xsd#kg_EquityMethodInvestmentsDistributionsNetPresentValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:to="lab_kg_EquityMethodInvestmentsDistributionsNetPresentValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_019ce734-5cd9-74cb-ac1a-704bf14e038a_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAxis" xlink:to="lab_us-gaap_BusinessAcquisitionAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_019ce734-5c52-76dc-a825-76d0c90d1201_totalLabel_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_label_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue_documentation_en-US" xlink:label="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Fixed Maturities, Continuous Unrealized Loss Position, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:href="kg-20260331.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_019ce734-5cd9-7f72-aa99-df42b025f699_terseLabel_en-US" xlink:label="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust European Hospital Liability Quota Share Agreement</link:label>
    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_label_en-US" xlink:label="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">AmTrust European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_documentation_en-US" xlink:label="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">AmTrust European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:href="kg-20260331.xsd#kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:to="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_019ce734-5c52-76c7-9ef9-bee02af6e21f_terseLabel_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Domain]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_label_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Domain]</link:label>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_documentation_en-US" xlink:label="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Cash and Investments, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:href="kg-20260331.xsd#kg_RestrictedCashAndInvestmentsTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:to="lab_kg_RestrictedCashAndInvestmentsTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_019ce734-5cd9-7a15-bc8b-e1ad69b4577f_terseLabel_en-US" xlink:label="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">As a percentage of total assets</link:label>
    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_label_en-US" xlink:label="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Percent of Assets Measured at Fair Value to Total Assets</link:label>
    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_documentation_en-US" xlink:label="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Percent of Assets Measured at Fair Value to Total Assets</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:href="kg-20260331.xsd#kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:to="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_019ce734-5ba1-7ff2-a562-6f5599242095_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Investment Income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeTextBlock" xlink:to="lab_us-gaap_InvestmentIncomeTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GrossPremiumsWrittenMember_019dcdb8-9e2d-7a5c-b76b-bb743fe371e0_terseLabel_en-US" xlink:label="lab_kg_GrossPremiumsWrittenMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Gross Premiums Written</link:label>
    <link:label id="lab_kg_GrossPremiumsWrittenMember_label_en-US" xlink:label="lab_kg_GrossPremiumsWrittenMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gross Premiums Written [Member]</link:label>
    <link:label id="lab_kg_GrossPremiumsWrittenMember_documentation_en-US" xlink:label="lab_kg_GrossPremiumsWrittenMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gross Premiums Written [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GrossPremiumsWrittenMember" xlink:href="kg-20260331.xsd#kg_GrossPremiumsWrittenMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GrossPremiumsWrittenMember" xlink:to="lab_kg_GrossPremiumsWrittenMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019ce734-5c52-77cb-8eb5-b31233c26688_verboseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Ownership percentage</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_019ce734-5c52-776f-9cca-11f9e7294753_terseLabel_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Beneficial Ownership</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage_label_en-US" xlink:label="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investment, Ownership Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquityMethodInvestmentOwnershipPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:to="lab_us-gaap_EquityMethodInvestmentOwnershipPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_019ce734-5ba0-7298-9f54-138a0c694b32_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Numerator:</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Available to Common Stockholders, Basic [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:to="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasicAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount_019ce734-5ba0-7046-862f-700900e48472_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for losses incurred but not reported ("IBNR")</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Incurred but Not Reported (IBNR) Claims, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:to="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseIncurredButNotReportedIBNRClaimsAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReconciliationtoNetIncomeLossAbstract_019ce734-5c52-75d3-82e5-60ff7b3c030b_terseLabel_en-US" xlink:label="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation to net loss from continuing operations</link:label>
    <link:label id="lab_kg_ReconciliationtoNetIncomeLossAbstract_label_en-US" xlink:label="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reconciliation to Net Income (Loss) [Abstract]</link:label>
    <link:label id="lab_kg_ReconciliationtoNetIncomeLossAbstract_documentation_en-US" xlink:label="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reconciliation to Net Income (Loss) [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReconciliationtoNetIncomeLossAbstract" xlink:href="kg-20260331.xsd#kg_ReconciliationtoNetIncomeLossAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReconciliationtoNetIncomeLossAbstract" xlink:to="lab_kg_ReconciliationtoNetIncomeLossAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_terseLabel_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:label id="lab_ecd_PeoActuallyPaidCompAmt_label_en-US" xlink:label="lab_ecd_PeoActuallyPaidCompAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">PEO Actually Paid Compensation Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PeoActuallyPaidCompAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PeoActuallyPaidCompAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PeoActuallyPaidCompAmt" xlink:to="lab_ecd_PeoActuallyPaidCompAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NumberOfNonIndependentDirectors_019ce734-5c52-7406-b965-02bec9c710ba_terseLabel_en-US" xlink:label="lab_kg_NumberOfNonIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of non-independent director</link:label>
    <link:label id="lab_kg_NumberOfNonIndependentDirectors_label_en-US" xlink:label="lab_kg_NumberOfNonIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Non-Independent Directors</link:label>
    <link:label id="lab_kg_NumberOfNonIndependentDirectors_documentation_en-US" xlink:label="lab_kg_NumberOfNonIndependentDirectors" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Number Of Non-Independent Directors</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NumberOfNonIndependentDirectors" xlink:href="kg-20260331.xsd#kg_NumberOfNonIndependentDirectors"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_NumberOfNonIndependentDirectors" xlink:to="lab_kg_NumberOfNonIndependentDirectors" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetManagementAgreementMember_019ce734-5c52-760e-b7be-08cb52f9064e_terseLabel_en-US" xlink:label="lab_kg_AssetManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Asset Management Agreement</link:label>
    <link:label id="lab_kg_AssetManagementAgreementMember_label_en-US" xlink:label="lab_kg_AssetManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Asset Management Agreement [Member]</link:label>
    <link:label id="lab_kg_AssetManagementAgreementMember_documentation_en-US" xlink:label="lab_kg_AssetManagementAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Asset Management Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_AssetManagementAgreementMember" xlink:href="kg-20260331.xsd#kg_AssetManagementAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetManagementAgreementMember" xlink:to="lab_kg_AssetManagementAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_019ce734-5ba0-77aa-9384-f4a3364fdf1b_totalLabel_en-US" xlink:label="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total restricted investments</link:label>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_label_en-US" xlink:label="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Restricted Investment, Net of Liabilities</link:label>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_documentation_en-US" xlink:label="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Restricted Investment, Net of Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RestrictedInvestmentNetOfLiabilities" xlink:href="kg-20260331.xsd#kg_RestrictedInvestmentNetOfLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedInvestmentNetOfLiabilities" xlink:to="lab_kg_RestrictedInvestmentNetOfLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_StatementScenarioAxis_019e039b-6ee4-7e43-8d10-562c0bef960e_terseLabel_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:label id="lab_srt_StatementScenarioAxis_label_en-US" xlink:label="lab_srt_StatementScenarioAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementScenarioAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementScenarioAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_StatementScenarioAxis" xlink:to="lab_srt_StatementScenarioAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member_019d33da-9605-777f-8d4c-cc5a49143b7e_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investment - preferred shares 3 and 4</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3 and 4 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 3 and 4</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3And4Member" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FoundingShareholdersMember_019ce734-5cd9-74b3-ab04-cd0d89872b08_terseLabel_en-US" xlink:label="lab_kg_FoundingShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Founding shareholders</link:label>
    <link:label id="lab_kg_FoundingShareholdersMember_label_en-US" xlink:label="lab_kg_FoundingShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Founding Shareholders [Member]</link:label>
    <link:label id="lab_kg_FoundingShareholdersMember_documentation_en-US" xlink:label="lab_kg_FoundingShareholdersMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Founding Shareholders [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FoundingShareholdersMember" xlink:href="kg-20260331.xsd#kg_FoundingShareholdersMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FoundingShareholdersMember" xlink:to="lab_kg_FoundingShareholdersMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealEstateInvestmentsAtEquityMethodMember_019ce734-5c52-72c0-8fe2-913e76352588_terseLabel_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Real estate investments at equity method</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtEquityMethodMember_label_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Equity Method [Member]</link:label>
    <link:label id="lab_kg_RealEstateInvestmentsAtEquityMethodMember_documentation_en-US" xlink:label="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Real Estate Investments At Equity Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:href="kg-20260331.xsd#kg_RealEstateInvestmentsAtEquityMethodMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:to="lab_kg_RealEstateInvestmentsAtEquityMethodMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_019ce734-5c52-7a64-a82f-fc9e58749832_terseLabel_en-US" xlink:label="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash and cash equivalents</link:label>
    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_label_en-US" xlink:label="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash And Cash Equivalents And Other [Member]</link:label>
    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_documentation_en-US" xlink:label="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cash And Cash Equivalents And Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CashAndCashEquivalentsAndOtherMember" xlink:href="kg-20260331.xsd#kg_CashAndCashEquivalentsAndOtherMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CashAndCashEquivalentsAndOtherMember" xlink:to="lab_kg_CashAndCashEquivalentsAndOtherMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock_019ce734-5c52-70e5-ae0f-3858a0b4fb8f_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for Loss and Loss Adjustment Expenses</link:label>
    <link:label id="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Future Policy Benefits and Unpaid Claims Disclosure [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:to="lab_us-gaap_LiabilityForFuturePolicyBenefitsAndUnpaidClaimsDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_019ce734-5cd9-72b0-a4c5-badd0f1b66ac_negatedLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, gross losses</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Loss</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:to="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_019ce734-5cd9-762c-86ce-2ef1ddf7fb7e_terseLabel_en-US" xlink:label="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income and net realized and unrealized investment gains</link:label>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_label_en-US" xlink:label="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income and Gain (Loss) on Investments, Net</link:label>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_documentation_en-US" xlink:label="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Investment Income and Gain (Loss) on Investments, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:href="kg-20260331.xsd#kg_InvestmentIncomeAndGainLossOnInvestmentsNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:to="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AllIndividualsMember_terseLabel_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Individuals</link:label>
    <link:label id="lab_ecd_AllIndividualsMember_label_en-US" xlink:label="lab_ecd_AllIndividualsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Individuals [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllIndividualsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllIndividualsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AllIndividualsMember" xlink:to="lab_ecd_AllIndividualsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_019ce734-5ba0-7507-a8df-61097cdcfc8e_terseLabel_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-term Debt, Type [Domain]</link:label>
    <link:label id="lab_us-gaap_LongtermDebtTypeDomain_label_en-US" xlink:label="lab_us-gaap_LongtermDebtTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Term Debt, Type [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LongtermDebtTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LongtermDebtTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LongtermDebtTypeDomain" xlink:to="lab_us-gaap_LongtermDebtTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_019ce734-5ba1-75f3-9c10-890bc2a5a2a1_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:label id="lab_us-gaap_FairValueDisclosuresAbstract_label_en-US" xlink:label="lab_us-gaap_FairValueDisclosuresAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value Disclosures [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueDisclosuresAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueDisclosuresAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueDisclosuresAbstract" xlink:to="lab_us-gaap_FairValueDisclosuresAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense_019ce734-5c52-729d-bc09-94f1e6384724_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">General and administrative expenses</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, General and Administrative Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationGeneralAndAdministrativeExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Name</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryIndName_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryIndName" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Individual Name</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryIndName" xlink:to="lab_ecd_ForgoneRecoveryIndName" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_terseLabel_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember_label_en-US" xlink:label="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-over-Year Change in Fair Value of Equity Awards Granted in Prior Years That are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:to="lab_ecd_ChngInFrValOfOutsdngAndUnvstdEqtyAwrdsGrntdInPrrYrsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_019d33da-9605-7cee-9d1c-3e9f845ee204_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private equity investment - preferred shares 1 and 2</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_label_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 1 and 2 [Member]</link:label>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock 1 and 2</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:to="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_019d33b6-d238-73c5-816d-e03c402eef16_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Contingent Receivable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_019d33d2-a3c1-7a36-a2de-30f6c620d024_verboseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Contingent receivable</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Asset</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationAsset"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationAsset" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_019ce734-5ba0-73ef-a351-ffbeba649775_terseLabel_en-US" xlink:label="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net cash used in discontinued operations</link:label>
    <link:label id="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations_label_en-US" xlink:label="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Operating Activity, Discontinued Operation</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:to="lab_us-gaap_CashProvidedByUsedInOperatingActivitiesDiscontinuedOperations" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_019ce734-5cd9-7e4a-b981-04938a90617a_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_label_en-US" xlink:label="lab_us-gaap_DisposalGroupClassificationAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Classification [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupClassificationAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupClassificationAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupClassificationAxis" xlink:to="lab_us-gaap_DisposalGroupClassificationAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1_019dbbc4-d8a9-787d-9205-d4ffc01fb1e4_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Distributions, increase in fair value</link:label>
    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1_label_en-US" xlink:label="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Contingent Consideration, Change in Contingent Consideration, Asset, Increase (Decrease)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:to="lab_us-gaap_BusinessCombinationContingentConsiderationArrangementsChangeInAmountOfContingentConsiderationAsset1" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_019ce734-5ba0-7840-91b3-ec3b855c7526_terseLabel_en-US" xlink:label="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">European Hospital Liability Quota Share</link:label>
    <link:label id="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_label_en-US" xlink:label="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:label id="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_documentation_en-US" xlink:label="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">European Hospital Liability Quota Share Agreement [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:href="kg-20260331.xsd#kg_EuropeanHospitalLiabilityQuotaShareAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:to="lab_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_019ce734-5cd9-744a-961f-fafac626fdb2_terseLabel_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reconciliation of cash and restricted cash reported within Condensed Consolidated Balance Sheets:</link:label>
    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_label_en-US" xlink:label="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_019ce734-5ba0-78a2-89ae-6e70c74b37d8_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:to="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis</link:label>
    <link:label id="lab_ecd_ErrCompAnalysisTextBlock_label_en-US" xlink:label="lab_ecd_ErrCompAnalysisTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneous Compensation Analysis [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompAnalysisTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompAnalysisTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompAnalysisTextBlock" xlink:to="lab_ecd_ErrCompAnalysisTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_terseLabel_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated</link:label>
    <link:label id="lab_ecd_Rule10b51ArrTrmntdFlag_label_en-US" xlink:label="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Rule 10b5-1 Arrangement Terminated [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_Rule10b51ArrTrmntdFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_Rule10b51ArrTrmntdFlag" xlink:to="lab_ecd_Rule10b51ArrTrmntdFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_EquityMethodInvestmentsInvesteeRevenue_019ce734-5c52-7b38-b6e5-529d922a6c0d_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investee Revenue</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsInvesteeRevenue_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments Investee Revenue</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsInvesteeRevenue_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments Investee Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:href="kg-20260331.xsd#kg_EquityMethodInvestmentsInvesteeRevenue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:to="lab_kg_EquityMethodInvestmentsInvesteeRevenue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_ErrCompRecoveryTable_terseLabel_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery</link:label>
    <link:label id="lab_ecd_ErrCompRecoveryTable_label_en-US" xlink:label="lab_ecd_ErrCompRecoveryTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Erroneously Awarded Compensation Recovery [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ErrCompRecoveryTable" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ErrCompRecoveryTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ErrCompRecoveryTable" xlink:to="lab_ecd_ErrCompRecoveryTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_019dcdb8-9e2d-7ddc-8786-c53345d0a117_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskBenchmarkDomain_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk Benchmark [Domain]</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLoss_019ce734-5ba1-744b-9415-f44f4fc01129_totalLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ce734-5ba1-7a0d-b738-508a5ca83184_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_019ce734-5ba1-761f-aba2-ead0311526cd_verboseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net loss</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_label_en-US" xlink:label="lab_us-gaap_NetIncomeLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLoss" xlink:to="lab_us-gaap_NetIncomeLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CollateralizedLoanObligationsMember_019ce734-5ba0-73bb-91fc-bf900acefb66_terseLabel_en-US" xlink:label="lab_us-gaap_CollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateralized loan obligations</link:label>
    <link:label id="lab_us-gaap_CollateralizedLoanObligationsMember_label_en-US" xlink:label="lab_us-gaap_CollateralizedLoanObligationsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Collateralized Loan Obligations [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CollateralizedLoanObligationsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CollateralizedLoanObligationsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CollateralizedLoanObligationsMember" xlink:to="lab_us-gaap_CollateralizedLoanObligationsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_019ce734-5c52-767f-ab82-9e2a421fdc53_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_label_en-US" xlink:label="lab_us-gaap_SegmentReportingInformationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting Information [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingInformationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingInformationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingInformationLineItems" xlink:to="lab_us-gaap_SegmentReportingInformationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_019ddea3-387e-7168-8151-9ef9e669932c_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Repurchase of common shares</link:label>
    <link:label id="lab_us-gaap_PaymentsForRepurchaseOfCommonStock_label_en-US" xlink:label="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Payments for Repurchase of Common Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForRepurchaseOfCommonStock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:to="lab_us-gaap_PaymentsForRepurchaseOfCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_TrdArrAdoptionDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adoption Date</link:label>
    <link:label id="lab_ecd_TrdArrAdoptionDate_label_en-US" xlink:label="lab_ecd_TrdArrAdoptionDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Adoption Date</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_TrdArrAdoptionDate" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_TrdArrAdoptionDate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TrdArrAdoptionDate" xlink:to="lab_ecd_TrdArrAdoptionDate" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_019ce734-5c52-7a06-99b9-b9f7503a9049_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Percentage of assets and liabilities associated with reinsurance business retroceded</link:label>
    <link:label id="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_label_en-US" xlink:label="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance, Assets And Liabilities, Retroceded, Percentage</link:label>
    <link:label id="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_documentation_en-US" xlink:label="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Reinsurance, Assets And Liabilities, Retroceded, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:href="kg-20260331.xsd#kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:to="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_019ce734-5ba0-76ff-805d-42d1149ec68b_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Lessee, operating lease, term of contract</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Term of Contract</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseTermOfContract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:to="lab_us-gaap_LesseeOperatingLeaseTermOfContract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019d33da-9605-7788-93fa-d24947fa40b6_terseLabel_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Term to Exit</link:label>
    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_label_en-US" xlink:label="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Measurement Input, Expected Term [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_MeasurementInputExpectedTermMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputExpectedTermMember" xlink:to="lab_us-gaap_MeasurementInputExpectedTermMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable_019ce734-5ba0-7687-8af8-07a582d29ebd_terseLabel_en-US" xlink:label="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Investments [Table]</link:label>
    <link:label id="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable_label_en-US" xlink:label="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Investments [Table]</link:label>
    <link:label id="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable_documentation_en-US" xlink:label="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Cash and Investments [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:href="kg-20260331.xsd#kg_ScheduleOfRestrictedCashAndInvestmentsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:to="lab_kg_ScheduleOfRestrictedCashAndInvestmentsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_019ce734-5cd9-7580-8655-4a3d43f7bf7d_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission rate, adjustment criteria, loss ratio ceiling</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Ceiling</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Adjustment Criteria, Loss Ratio Ceiling</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:href="kg-20260331.xsd#kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:to="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioCeiling" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_019ce734-5c52-7674-8d2f-114b524b2276_verboseLabel_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">(Accumulated deficit) retained earnings</link:label>
    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_label_en-US" xlink:label="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Retained Earnings (Accumulated Deficit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RetainedEarningsAccumulatedDeficit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:to="lab_us-gaap_RetainedEarningsAccumulatedDeficit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock_019df2db-7158-7567-b751-eecb1016b7e0_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Class of Treasury Stock</link:label>
    <link:label id="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Class of Treasury Stock [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfTreasuryStockByClassTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:to="lab_us-gaap_ScheduleOfTreasuryStockByClassTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_019ce734-5c52-70c9-ada4-5efd99037b6b_terseLabel_en-US" xlink:label="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">BBB+, BBB, BBB-</link:label>
    <link:label id="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_label_en-US" xlink:label="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, BBB Plus, BBB, BBB Minus Rating [Member]</link:label>
    <link:label id="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_documentation_en-US" xlink:label="lab_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Standard &amp; Poor's, BBB Plus, BBB, BBB Minus Rating [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember" xlink:href="kg-20260331.xsd#kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember"/>
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    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_terseLabel_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested</link:label>
    <link:label id="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember_label_en-US" xlink:label="lab_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Year-end Fair Value of Equity Awards Granted in Covered Year that are Outstanding and Unvested [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_YrEndFrValOfEqtyAwrdsGrntdInCvrdYrOutsdngAndUnvstdMember"/>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses_019ce734-5c52-7521-a75b-c1737f3be395_terseLabel_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other losses</link:label>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses_label_en-US" xlink:label="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group, Including Discontinued Operation, Foreign Currency Translation Gains (Losses)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses"/>
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    <link:label id="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod_019ce734-5cd9-7b81-b305-deb9a188650c_terseLabel_en-US" xlink:label="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Equity method investments</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod_label_en-US" xlink:label="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Recorded with Equity Method</link:label>
    <link:label id="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod_documentation_en-US" xlink:label="lab_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Method Investments, Recorded with Equity Method</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:href="kg-20260331.xsd#kg_EquityMethodInvestmentsRecordedWithEquityMethod"/>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_019d3d3d-27cb-7152-8b44-646ab8377f2e_terseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Accumulated Amortization at March&#160;31, 2026</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Assets, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsNetAbstract"/>
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    <link:label id="lab_us-gaap_StatementTable_019ce734-5c52-7064-b713-2a8488659d02_terseLabel_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:label id="lab_us-gaap_StatementTable_label_en-US" xlink:label="lab_us-gaap_StatementTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statement [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatementTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatementTable"/>
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    <link:label id="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:to="lab_us-gaap_ScheduleOfBusinessAcquisitionsByAcquisitionTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities_019ce734-5ba0-797f-90a8-8387091c4909_terseLabel_en-US" xlink:label="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from maturities, paydowns and calls of fixed maturities</link:label>
    <link:label id="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities_label_en-US" xlink:label="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds From Maturities, Prepayments And Calls Of Debt Securities, Investing Activities</link:label>
    <link:label id="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities_documentation_en-US" xlink:label="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Proceeds From Maturities, Prepayments And Calls Of Debt Securities, Investing Activities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities" xlink:href="kg-20260331.xsd#kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities" xlink:to="lab_kg_ProceedsFromMaturitiesPrepaymentsAndCallsOfDebtSecuritiesInvestingActivities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_019ce734-5c52-7389-a31e-225984d315a3_terseLabel_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adjustments to reconcile net loss to net cash flows from operating activities:</link:label>
    <link:label id="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_AdjustmentsToReconcileNetIncomeLossToCashProvidedByUsedInOperatingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity [Abstract]</link:label>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_019ce734-5ba0-7e67-a8ba-d9232f794ff7_terseLabel_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash flows from financing activities:</link:label>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_label_en-US" xlink:label="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract"/>
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    <link:label id="lab_kg_GainLossOnEquityMethodInvestments_019ce734-5c52-779e-9ca8-a1024a5c58e8_terseLabel_en-US" xlink:label="lab_kg_GainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Realized and unrealized gains (losses)</link:label>
    <link:label id="lab_kg_GainLossOnEquityMethodInvestments_label_en-US" xlink:label="lab_kg_GainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Equity Method Investments</link:label>
    <link:label id="lab_kg_GainLossOnEquityMethodInvestments_documentation_en-US" xlink:label="lab_kg_GainLossOnEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Equity Method Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GainLossOnEquityMethodInvestments" xlink:href="kg-20260331.xsd#kg_GainLossOnEquityMethodInvestments"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_019ce734-5c52-793a-8592-f6a9a48f2b60_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Amortized Cost, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:to="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAmortizedCostAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_019ce734-5c52-741f-a843-b05f74e2a673_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment, Type [Extensible Enumeration]</link:label>
    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_label_en-US" xlink:label="lab_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Type [Extensible Enumeration]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentTypeExtensibleEnumeration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentTypeExtensibleEnumeration"/>
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    <link:label id="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock_label_en-US" xlink:label="lab_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Assets Measured on Recurring Basis, Unobservable Input Reconciliation [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationTextBlock"/>
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    <link:label id="lab_ecd_AllAdjToCompMember_terseLabel_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation</link:label>
    <link:label id="lab_ecd_AllAdjToCompMember_label_en-US" xlink:label="lab_ecd_AllAdjToCompMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">All Adjustments to Compensation [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AllAdjToCompMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AllAdjToCompMember"/>
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    <link:label id="lab_dei_AmendmentFlag_019ce734-5c52-783c-9ee1-b6b4df376be5_terseLabel_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
    <link:label id="lab_dei_AmendmentFlag_label_en-US" xlink:label="lab_dei_AmendmentFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Amendment Flag</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_019ce734-5c52-7558-b088-eb4a4d25561b_terseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Fair Value, Fiscal Year Maturity [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_019ce734-5c52-7535-a1b3-011c8ba9058f_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares issuable under incentive plans (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Authorized</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAuthorized"/>
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    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock_019ce734-5ba1-75a1-a9a8-4d71078407dd_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Intangible Assets Acquired</link:label>
    <link:label id="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfAcquiredFiniteLivedIntangibleAssetsByMajorClassTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Acquired Finite-Lived Intangible Assets by Major Class [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019ce734-5cd9-7e9a-8c11-dddc1d404958_verboseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses (includes $514,149 and $554,507 from related parties in 2026 and 2025, respectively)</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019ce734-5cd9-7031-8ba4-3054970bbb78_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019ce734-5cd9-756e-9269-ead44462920c_totalLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Reserve for loss and LAE</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019ce734-5cd9-7b67-8a4d-001386c14388_periodStartLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Gross loss and LAE reserves, January 1</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_019ce734-5cd9-72bc-9a04-dee4e418ac87_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Gross loss and LAE reserves, March 31</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Claims and Claims Adjustment Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonValue_label_en-US" xlink:label="lab_us-gaap_TreasuryStockCommonValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Common, Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TreasuryStockCommonValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TreasuryStockCommonValue"/>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_019ce734-5cd9-780e-b64d-06b1e506323a_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Privately held preferred stocks</link:label>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember_documentation_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Privately Held Equity Investments in Preferred Stock</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember" xlink:href="kg-20260331.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStockMember"/>
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    <link:label id="lab_ecd_TrdArrTerminationDate_terseLabel_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Termination Date</link:label>
    <link:label id="lab_ecd_TrdArrTerminationDate_label_en-US" xlink:label="lab_ecd_TrdArrTerminationDate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Trading Arrangement Termination Date</link:label>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_019ce734-5ba0-74ee-a48f-b008a5b08ef0_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating lease, weighted average discount rate</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent"/>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_019ce734-5c52-7968-85f2-86c342bd7e76_terseLabel_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average number of common shares - basic (in shares)</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_label_en-US" xlink:label="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Weighted Average Number of Shares Outstanding, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_WeightedAverageNumberOfSharesOutstandingBasic"/>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_019ce734-5ba1-7895-8b4d-81625e8627b7_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Elements Used in Calculating Basic and Diluted Earnings Per Common Share</link:label>
    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Earnings Per Share, Basic and Diluted [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock"/>
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    <link:label id="lab_kg_ValuationTechniqueDiscountedCashFlowAndOptionPricingModelMember_019d33d1-2455-7a2d-91cb-145e89905689_terseLabel_en-US" xlink:label="lab_kg_ValuationTechniqueDiscountedCashFlowAndOptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounted cash flows &amp; option pricing models</link:label>
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    <link:label id="lab_kg_ValuationTechniqueDiscountedCashFlowAndOptionPricingModelMember_documentation_en-US" xlink:label="lab_kg_ValuationTechniqueDiscountedCashFlowAndOptionPricingModelMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Valuation Technique, Discounted Cash Flow and Option Pricing Model</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ValuationTechniqueDiscountedCashFlowAndOptionPricingModelMember" xlink:href="kg-20260331.xsd#kg_ValuationTechniqueDiscountedCashFlowAndOptionPricingModelMember"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_019ce734-5c52-772b-bc76-dc38b7159b48_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionDomain" xlink:to="lab_us-gaap_RelatedPartyTransactionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_019ce734-5c52-7b5d-8147-e9ca460835ca_terseLabel_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:label id="lab_us-gaap_SegmentReportingAbstract_label_en-US" xlink:label="lab_us-gaap_SegmentReportingAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Segment Reporting [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SegmentReportingAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SegmentReportingAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SegmentReportingAbstract" xlink:to="lab_us-gaap_SegmentReportingAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseExpense_019ce734-5c52-79f6-b131-8d359992de73_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasing expense</link:label>
    <link:label id="lab_us-gaap_OperatingLeaseExpense_label_en-US" xlink:label="lab_us-gaap_OperatingLeaseExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Lease, Expense</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLeaseExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLeaseExpense"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLeaseExpense" xlink:to="lab_us-gaap_OperatingLeaseExpense" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_019ce734-5cd9-79f8-a142-f288ce3d6a3c_terseLabel_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
    <link:label id="lab_us-gaap_DebtDisclosureAbstract_label_en-US" xlink:label="lab_us-gaap_DebtDisclosureAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Disclosure [Abstract]</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtDisclosureAbstract" xlink:to="lab_us-gaap_DebtDisclosureAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_019e039b-6ee4-7d30-9816-c992596353c6_terseLabel_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:label id="lab_srt_ScenarioUnspecifiedDomain_label_en-US" xlink:label="lab_srt_ScenarioUnspecifiedDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Scenario [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ScenarioUnspecifiedDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ScenarioUnspecifiedDomain"/>
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    <link:label id="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent_019ce734-5c52-7c4f-9c1f-259a4fe30c82_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Amounts reclassified from AOCI to net loss, net of tax</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReclassificationFromAociCurrentPeriodBeforeTaxAttributableToParent"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_019ce734-5c52-7c99-8e78-bf80f271f456_totalLabel_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Fixed maturities, net</link:label>
    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Realized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss"/>
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    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax_019ce734-5ba0-7632-8e18-32104fae59c3_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized holdings losses on AFS fixed maturities</link:label>
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    <link:label id="lab_kg_OtherPrivatelyHeldInvestmentsMember_019ce734-5c52-722c-b6ea-306840b309c4_terseLabel_en-US" xlink:label="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Privately held equity investments</link:label>
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    <link:label id="lab_kg_OtherPrivatelyHeldInvestmentsMember_documentation_en-US" xlink:label="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Privately Held Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherPrivatelyHeldInvestmentsMember" xlink:href="kg-20260331.xsd#kg_OtherPrivatelyHeldInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherPrivatelyHeldInvestmentsMember" xlink:to="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_019ce734-5c52-79a8-8230-c2286c39693d_terseLabel_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:label id="lab_srt_ConsolidatedEntitiesAxis_label_en-US" xlink:label="lab_srt_ConsolidatedEntitiesAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidated Entities [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ConsolidatedEntitiesAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ConsolidatedEntitiesAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ConsolidatedEntitiesAxis" xlink:to="lab_srt_ConsolidatedEntitiesAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_019ce734-5ba0-7258-bdc8-a8a992d88c52_terseLabel_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Common shares, par value (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_label_en-US" xlink:label="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Common Stock, Par or Stated Value Per Share</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CommonStockParOrStatedValuePerShare"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CommonStockParOrStatedValuePerShare" xlink:to="lab_us-gaap_CommonStockParOrStatedValuePerShare" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVentureMember_019d33da-9605-745e-a7de-18db82d94ec9_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVentureMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Ventures</link:label>
    <link:label id="lab_kg_SilverstoneVentureMember_label_en-US" xlink:label="lab_kg_SilverstoneVentureMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Silverstone Venture [Member]</link:label>
    <link:label id="lab_kg_SilverstoneVentureMember_documentation_en-US" xlink:label="lab_kg_SilverstoneVentureMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Silverstone Venture</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SilverstoneVentureMember" xlink:href="kg-20260331.xsd#kg_SilverstoneVentureMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_SilverstoneVentureMember" xlink:to="lab_kg_SilverstoneVentureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet_019ce734-5cd9-78f0-a9b0-9139860f36e6_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Loss and LAE ceded</link:label>
    <link:label id="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet_label_en-US" xlink:label="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Policyholder Benefits and Claims Incurred, Assumed and Ceded</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceCostsAndRecoveriesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:to="lab_us-gaap_ReinsuranceCostsAndRecoveriesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_019ce734-5cd9-7857-8365-b4a812819129_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Income tax expense related to components of other comprehensive loss</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Tax, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1"/>
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    <link:label id="lab_kg_TerryAndLukeLedbetterMember_019ddfa9-29b2-7629-94e4-15a1161142b8_terseLabel_en-US" xlink:label="lab_kg_TerryAndLukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Terry and Luke Ledbetter</link:label>
    <link:label id="lab_kg_TerryAndLukeLedbetterMember_label_en-US" xlink:label="lab_kg_TerryAndLukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Terry and Luke Ledbetter [Member]</link:label>
    <link:label id="lab_kg_TerryAndLukeLedbetterMember_documentation_en-US" xlink:label="lab_kg_TerryAndLukeLedbetterMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Terry and Luke Ledbetter</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TerryAndLukeLedbetterMember" xlink:href="kg-20260331.xsd#kg_TerryAndLukeLedbetterMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_TerryAndLukeLedbetterMember" xlink:to="lab_kg_TerryAndLukeLedbetterMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LoanAgreementMember_019ce734-5cd9-7758-b3c2-e1efd7574f17_terseLabel_en-US" xlink:label="lab_kg_LoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loan Agreement</link:label>
    <link:label id="lab_kg_LoanAgreementMember_label_en-US" xlink:label="lab_kg_LoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loan Agreement [Member]</link:label>
    <link:label id="lab_kg_LoanAgreementMember_documentation_en-US" xlink:label="lab_kg_LoanAgreementMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Loan Agreement</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LoanAgreementMember" xlink:href="kg-20260331.xsd#kg_LoanAgreementMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LoanAgreementMember" xlink:to="lab_kg_LoanAgreementMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_019ce734-5cd9-7d27-bb61-fe4e28fe5838_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign currency translation adjustment</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Comprehensive Income (Loss), Foreign Currency Transaction and Translation Adjustment, Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:to="lab_us-gaap_OtherComprehensiveIncomeLossForeignCurrencyTransactionAndTranslationAdjustmentNetOfTax" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_InsiderTradingArrLineItems_label_en-US" xlink:label="lab_ecd_InsiderTradingArrLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insider Trading Arrangements [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTradingArrLineItems" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTradingArrLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTradingArrLineItems" xlink:to="lab_ecd_InsiderTradingArrLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_019ce734-5cd9-7602-a96e-be456bfc1c3b_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Reinsurance Recoverable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInReinsuranceRecoverable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:to="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentIncomeInterestAndDividend_019ce734-5cd9-7573-aa6a-b05fd2730e90_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterestAndDividend" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeInterestAndDividend_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeInterestAndDividend" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Interest and Dividend</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeInterestAndDividend" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeInterestAndDividend"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeInterestAndDividend" xlink:to="lab_us-gaap_InvestmentIncomeInterestAndDividend" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate_019ce734-5cd9-710d-b558-8789f17ca011_terseLabel_en-US" xlink:label="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective yield</link:label>
    <link:label id="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate_label_en-US" xlink:label="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Receivable with Imputed Interest, Effective Yield (Interest Rate)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:to="lab_us-gaap_ReceivableWithImputedInterestEffectiveYieldInterestRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Liabilities_019ce734-5c52-75fd-b2b8-498ad96c67f5_totalLabel_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total liabilities</link:label>
    <link:label id="lab_us-gaap_Liabilities_label_en-US" xlink:label="lab_us-gaap_Liabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Liabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Liabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Liabilities" xlink:to="lab_us-gaap_Liabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet_019ce734-5c52-7380-bb3a-6bb4803242d4_terseLabel_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet_label_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Group Including Discontinued Operation Investment Income, Net</link:label>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet_documentation_en-US" xlink:label="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Disposal Group Including Discontinued Operation Investment Income, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet" xlink:href="kg-20260331.xsd#kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet" xlink:to="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_019ce734-5cd9-7324-98a4-490014aa3fa6_totalLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total securities with single maturities, amortized cost</link:label>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Securities, Available-for-Sale, Maturity, Allocated and Single Maturity Date, Amortized Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis"/>
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    <link:label id="lab_us-gaap_InvestmentIncomeNet_019ce734-5c52-7b36-8292-a4c45cf7ab7f_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeNet_019ce734-5c52-719f-b6bd-2cafc8e7334e_totalLabel_en-US" xlink:label="lab_us-gaap_InvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net investment income</link:label>
    <link:label id="lab_us-gaap_InvestmentIncomeNet_label_en-US" xlink:label="lab_us-gaap_InvestmentIncomeNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment Income, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentIncomeNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentIncomeNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InvestmentIncomeNet" xlink:to="lab_us-gaap_InvestmentIncomeNet" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_terseLabel_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost</link:label>
    <link:label id="lab_ecd_PnsnAdjsPrrSvcCstMember_label_en-US" xlink:label="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Pension Adjustments Prior Service Cost [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_PnsnAdjsPrrSvcCstMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_PnsnAdjsPrrSvcCstMember" xlink:to="lab_ecd_PnsnAdjsPrrSvcCstMember" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_terseLabel_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement</link:label>
    <link:label id="lab_ecd_MtrlTermsOfTrdArrTextBlock_label_en-US" xlink:label="lab_ecd_MtrlTermsOfTrdArrTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Material Terms of Trading Arrangement [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_MtrlTermsOfTrdArrTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_MtrlTermsOfTrdArrTextBlock"/>
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