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    <link:label id="lab_us-gaap_InvestmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investment, Policy [Policy Text Block]</link:label>
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    <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>
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    <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>
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    <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>
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    <link:label id="lab_us-gaap_AdditionalPaidInCapitalMember_4ff2ef25-43ec-44b1-8f3a-5c771acd5815_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>
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    <link:label id="lab_us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_3fac6dd9-4a41-4f06-aef0-36c1ce849d53_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>
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    <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"/>
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    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2019Member_2b3f27a5-0431-4f45-ba7d-952c8cc2ca5c_terseLabel_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2019Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2019</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfRelatedPartyTransactionsTableTextBlock_167d5f5d-9f11-4f19-837e-cae6b6f08d2a_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>
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    <link:label id="lab_us-gaap_FairValueByBalanceSheetGroupingTextBlock_b39ba255-2d59-475b-b2ef-d0c7ad240d09_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>
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    <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>
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    <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-20251231.xsd#kg_NumberOfNonIndependentDirectors"/>
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    <link:label id="lab_us-gaap_ScheduleOfStockByClassTable_544171e5-4c4c-486f-a4cb-128cca6374ea_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">Stock, Class of Stock [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_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock_63528d16-988b-4847-82b0-466ccd320bd9_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Statutory Capital and Surplus and Statutory Net Income (Loss) of Principal Operating Subsidiaries</link:label>
    <link:label id="lab_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock_label_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practices Disclosure [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatutoryAccountingPracticesDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock" xlink:to="lab_us-gaap_StatutoryAccountingPracticesDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale_ca57b57a-0dd9-4323-afee-17b71cf0529d_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale" 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_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale" 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, Assets Held For Sale</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale" 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, Assets Held For Sale</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale" xlink:href="kg-20251231.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAssetsHeldForSale" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionCollateralHeldByRelatedParty_5f10cb94-1a58-4555-bad3-6237c0da19b7_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-20251231.xsd#kg_RelatedPartyTransactionCollateralHeldByRelatedParty"/>
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    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_3a88ca35-60e9-4a4d-9c98-a9e64caf6259_totalLabel_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total current tax (benefit) expense</link:label>
    <link:label id="lab_us-gaap_CurrentIncomeTaxExpenseBenefit_label_en-US" xlink:label="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Current Income Tax Expense (Benefit)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CurrentIncomeTaxExpenseBenefit"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:to="lab_us-gaap_CurrentIncomeTaxExpenseBenefit" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AssetsOfDisposalGroupIncludingDiscontinuedOperation_b6775db7-62e5-48a8-b842-afb6587cb47a_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_f5b8ede9-9005-4124-b76d-bfe9c631a6f5_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">Total 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_d74f3c41-f3b8-4577-9e29-1dae7ff1a858_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_019cdeee-36e8-739d-9640-9225c20c2c69_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_5c21a531-d4f1-4f6f-8318-5aba28bda94a_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_c7888160-17d5-4442-a1ad-84b504f3e8d6_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_ConsolidationPolicyTextBlock_e684505e-f536-4d44-881d-91999fe9692a_terseLabel_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Basis of Reporting and Consolidation</link:label>
    <link:label id="lab_us-gaap_ConsolidationPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Consolidation, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConsolidationPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConsolidationPolicyTextBlock" xlink:to="lab_us-gaap_ConsolidationPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeStockOptionMember_40fb9807-d875-478a-9817-6f5997e23306_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">Share 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_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges_019cbfb5-3140-7904-8d20-07ab3e1e32e5_negatedTerseLabel_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Favorable PPD reinsurance</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges_label_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges" 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 Decrease, Net of Commission Changes</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges_documentation_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges" 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 Decrease, Net of Commission Changes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges" xlink:href="kg-20251231.xsd#kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges" xlink:to="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodDecreaseNetOfCommissionChanges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_ea3630bc-976b-49b5-925b-b55696f87e89_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfPropertyPlantAndEquipmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:to="lab_us-gaap_ScheduleOfPropertyPlantAndEquipmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock_8c3ba771-f237-4b9a-a7e0-dfbeac8e943e_terseLabel_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" 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_CashAndCashEquivalentsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash and Cash Equivalents, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAndCashEquivalentsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:to="lab_us-gaap_CashAndCashEquivalentsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_ec1b1100-411f-4327-9c16-3bcee745864f_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for income taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaid_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaid" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid</link:label>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTextBlock_734e755d-27fc-4c50-acad-78e0faa0da8d_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Depreciable Fixed Assets</link:label>
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    <link:label id="lab_kg_MeasurementInputChangeInGuidelinePublicCompanyTICMember_019cdeea-0fa7-7f9f-9019-c6ab45a01bb8_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>
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    <link:label id="lab_us-gaap_FundsHeldUnderReinsuranceAgreementsAsset_aa1951ff-0855-44f0-b64b-f1b95c43d440_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: 2025 - $2)</link:label>
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    <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>
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    <link:label id="lab_us-gaap_PremiumsReceivableAtCarryingValue_1cc5174f-b9e6-4f82-98cb-596ef9cb9f5f_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 $2 from related parties in 2025. Allowance for expected credit losses: 2025 - $14)</link:label>
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    <link:label id="lab_us-gaap_PortionAtFairValueFairValueDisclosureMember_eb82a8a5-6480-44c3-8f2d-3c015812572f_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>
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    <link:label id="lab_srt_MaximumMember_ab86e260-4b56-425c-9fe9-c02e2f68daa7_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_019cdf6c-a838-70ac-879c-384b6dca566c_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"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_965df6f3-9d4f-429c-8682-2da4ba3f9952_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total exercisable (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" 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, Options, Exercisable, Weighted Average Exercise Price</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsExercisableWeightedAverageExercisePrice"/>
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    <link:label id="lab_kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets_ebf8cec6-1331-4ddb-af59-480d31597fd3_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-20251231.xsd#kg_PercentOfAssetsMeasuredAtFairValueToTotalAssets"/>
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    <link:label id="lab_kg_AmtrustEuropeanHospitalLiabilityQuotaShareAgreementMember_f6eda7b3-30d8-40d4-bbd6-0280f43bce39_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-20251231.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_us-gaap_PolicyholderBenefitsAndClaimsIncurredNetAbstract_15a192cc-15f9-4b24-a755-2090ba1c3141_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"/>
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    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_73005884-10ae-490a-9e05-dcb64512dde7_terseLabel_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Collateral</link:label>
    <link:label id="lab_us-gaap_DebtInstrumentCollateralAmount_label_en-US" xlink:label="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Debt Instrument, Collateral Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtInstrumentCollateralAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentCollateralAmount" xlink:to="lab_us-gaap_DebtInstrumentCollateralAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_KestrelGroupMember_019b0161-beb7-7460-b0df-837846645ee5_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-20251231.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_us-gaap_RestrictedStockMember_40517662-cee6-4e1f-ade4-d2c6c91ad703_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 Shares</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_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_c3525e89-d491-4dbd-a12f-bde362515ec8_verboseLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net adverse PPD for Legacy Reinsurance Segment</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_019b01fa-626c-7610-9074-a0b4155a590a_netLabel_en-US" xlink:label="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net adverse PPD reinsurance</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_b0fbc17c-53b6-4e4d-a78a-d38bf67c497f_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 Diversified Reinsurance adverse PPD</link:label>
    <link:label id="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges_55dedeb0-0b01-49a0-bef2-a160d754e70f_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 favorable 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-20251231.xsd#kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" xlink:to="lab_kg_LiabilityforUnpaidClaimsandClaimsAdjustmentExpensePeriodIncreaseDecreaseNetofCommissionChanges" 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_24b53063-da75-445b-bead-04647685ea8a_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_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_86871a82-dc5d-435d-9aeb-41c240141d97_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Share-based Compensation Arrangements by Share-based Payment Award [Table]</link:label>
    <link:label id="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_label_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:to="lab_us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock_45ccfe07-ad02-43b2-8f5f-1e3183faa4c4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Restricted Share Awards</link:label>
    <link:label id="lab_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement, Restricted Stock and Restricted Stock Unit, Activity [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfSharebasedCompensationRestrictedStockAndRestrictedStockUnitsActivityTableTextBlock" 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_bf754ef9-df6b-41a3-a468-162242ca48d4_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_96a6df1c-cefd-4fe9-b8dd-22a0e737fb3b_terseLabel_en-US" xlink:label="lab_srt_ExternalCreditRatingStandardPoorsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Rating [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>
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    <link:label id="lab_us-gaap_DebtInstrumentTable_b1457a2c-eb94-4a35-be57-97346ffcec24_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>
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    <link:label id="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock_019cbc59-593f-7b0d-bb08-b7acff9aad1d_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCashFlowSupplementalDisclosuresTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income Tax Paid</link:label>
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    <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-20251231.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_dei_DocumentFiscalPeriodFocus_1e2cc6e8-6b9d-45fe-bd33-f5ac6c49c703_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_da6db534-61bc-4f23-9b70-31600f09e3ba_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"/>
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    <link:label id="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill_9f6c2eb2-ffe9-44cf-9c49-8adf46d68050_terseLabel_en-US" xlink:label="lab_us-gaap_IntangibleAssetsNetIncludingGoodwill" 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_IntangibleAssetsNetIncludingGoodwill_d4012046-5f92-4fba-8a32-d5a8473975ec_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_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_ShortDurationInsuranceContractsMinimumLossesPurchased_53b849c3-71b9-4b95-8d53-40c42d1e8bc4_terseLabel_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractsMinimumLossesPurchased" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Purchase significant reinsurance for losses above</link:label>
    <link:label id="lab_kg_ShortDurationInsuranceContractsMinimumLossesPurchased_label_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractsMinimumLossesPurchased" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short Duration Insurance Contracts, Minimum Losses Purchased</link:label>
    <link:label id="lab_kg_ShortDurationInsuranceContractsMinimumLossesPurchased_documentation_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractsMinimumLossesPurchased" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Short Duration Insurance Contracts, Minimum Losses Purchased</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShortDurationInsuranceContractsMinimumLossesPurchased" xlink:href="kg-20251231.xsd#kg_ShortDurationInsuranceContractsMinimumLossesPurchased"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShortDurationInsuranceContractsMinimumLossesPurchased" xlink:to="lab_kg_ShortDurationInsuranceContractsMinimumLossesPurchased" 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_019b02a5-3db2-7936-a2c7-7839cc6580ed_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_kg_ScheduleofFixedMaturitiesTableLineItems_019b0101-b6d5-7452-97b4-fa6676e6a350_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-20251231.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_IncomeLossFromContinuingOperationsPerBasicShare_7e6a4e8d-08c9-4ccb-8d34-3382facf0368_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 earnings (loss) from continuing operations per share attributable to Kestrel common 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_InvestmentsNetUnrealizedGainLoss_170395b3-5baa-4e17-b834-da8530cf2755_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-20251231.xsd#kg_InvestmentsNetUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InvestmentsNetUnrealizedGainLoss" xlink:to="lab_kg_InvestmentsNetUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AwardTypeAxis_b48c3b93-44a2-4f4e-9e2d-69cf1a684e01_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 [Axis]</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_kg_InterestAndAmortizationExpensesNet_ea126eb2-adf4-4697-aca9-23bb71d3d007_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_2bca29f2-cafb-4b8b-abc3-be92d106a665_negatedTerseLabel_en-US" xlink:label="lab_kg_InterestAndAmortizationExpensesNet" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" 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-20251231.xsd#kg_InterestAndAmortizationExpensesNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InterestAndAmortizationExpensesNet" xlink:to="lab_kg_InterestAndAmortizationExpensesNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AccumulatedTranslationAdjustmentMember_39b58daf-1179-49cb-af83-4586d615ddc8_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 adjustments</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_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_019ce34a-8dc9-7f0b-b3e6-b21098e45b9d_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Selected Financial Information, Pro Forma</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionProFormaInformationTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:to="lab_us-gaap_BusinessAcquisitionProFormaInformationTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_EquityMethodInvesteeNameDomain_9ac953b1-c09e-48a1-bbce-44bc652f492e_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_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy_a3d176d9-77d1-44db-ba90-1506d9e11491_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" 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_ShareBasedCompensationOptionAndIncentivePlansPolicy_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Share-Based Payment Arrangement [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:to="lab_us-gaap_ShareBasedCompensationOptionAndIncentivePlansPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_TradingSymbol_5e574349-da46-480b-8b2e-a056518ee2e9_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_ecb21199-ae20-4d49-ae89-76b374ff9031_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">2029</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"/>
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    <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>
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    <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>
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    <link:label id="lab_dei_EntityAddressCityOrTown_b15fe0df-9f01-4d68-9e2d-54315e79eae5_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>
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    <link:label id="lab_us-gaap_EffectOfExchangeRateOnCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_bfa4eb5c-e90a-4259-95df-998b864aea86_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</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsNet_6f0d7e57-2336-47c0-97cf-ef4551a704af_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets, net</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsNet" xlink:to="lab_us-gaap_DeferredTaxAssetsNet" 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>
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    <link:label id="lab_us-gaap_RestrictedStockUnitsRSUMember_c734d93a-5602-4e11-b624-22636667ef6e_terseLabel_en-US" xlink:label="lab_us-gaap_RestrictedStockUnitsRSUMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">RSUs</link:label>
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    <link:label id="lab_kg_DebtInstrumentPriorNoticeRedemptionPeriodStartDate_5b53b4ab-201d-4824-91d7-eb3972a5586a_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>
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    <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>
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    <link:label id="lab_us-gaap_BusinessCombinationConsiderationTransferred1_9325d1ee-6a94-4544-94f2-f15531da1585_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>
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    <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>
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    <link:label id="lab_us-gaap_StatutoryAccountingPracticesLineItems_988471e5-6639-4014-833c-fcde9d142d80_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practices [Line Items]</link:label>
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    <link:label id="lab_dei_EntityEmergingGrowthCompany_eadd2ae9-cddd-4584-863b-1b2448c5a4d1_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>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearThree_e511d9b7-6643-4c30-b2fc-3313980f8a51_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearThree" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 3</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor_e32af345-14c5-4ad6-be6f-a34ec2c71f25_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRateAdjustmentCriteriaLossRatioFloor" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission rate, adjustment criteria, loss ratio floor</link:label>
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    <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-20251231.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_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_kg_RelatedPartyTransactionAccruedInterestOnCollateralHeldByRelatedParty_5b6c7c63-782f-4942-b0ff-10157176051a_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-20251231.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_DeferredFinanceCostsNet_1f0f39b7-d5bc-4a54-8d5c-3c2f019bf428_verboseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsNet" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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_ShortdurationInsuranceContractsAccidentYear2014Member_90c0c096-cc0f-4b3d-8eae-7d9fb33b9a29_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2014</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Accident Year 2014 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2014Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_1760d4de-d95e-42a1-b2c6-5957cf7efb82_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_e83b7cd8-4ea4-4571-b8ad-5bc42c139bbc_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 year</link:label>
    <link:label id="lab_us-gaap_RestrictedCashAndCashEquivalents_5fa76212-e473-4423-95be-e35c286703f2_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_FixedMaturitiesContinuousUnrealizedLossPosition12MonthsorLongerAccumulatedLoss_bce38197-97bc-44b4-869d-a501a3536e6a_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-20251231.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_kg_AUMReinsuranceSegmentMember_019c8f28-b471-71b8-8b91-344afab32af4_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-20251231.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_kg_UnderwritingIncomeLossNet_7cf4a0d5-02cc-4664-97d2-907c6108d29a_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-20251231.xsd#kg_UnderwritingIncomeLossNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_UnderwritingIncomeLossNet" xlink:to="lab_kg_UnderwritingIncomeLossNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_6df39ce7-58a9-45d3-a5fb-d55756ce9678_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_b123089f-1f4c-4851-8370-32023d62af0b_periodStartLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Outstanding shares, beginning balance (in shares)</link:label>
    <link:label id="lab_us-gaap_CommonStockSharesOutstanding_aa25df9a-329a-4174-9670-f68134e5001d_periodEndLabel_en-US" xlink:label="lab_us-gaap_CommonStockSharesOutstanding" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding shares, ending balance (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_c43fbc89-d4ae-4a5a-bfe5-7454e734066b_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_d2d4adbc-0df4-49f7-87b7-f18fafb5ea13_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_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock_e7dde84a-ad02-4f51-a14f-4291e3221c4c_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Changes in Common Shares Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Common Stock Outstanding Roll Forward [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfCommonStockOutstandingRollForwardTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_61fcc453-a200-444e-8980-064789d11aa9_terseLabel_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">(Decrease) increase in valuation allowance</link:label>
    <link:label id="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount_label_en-US" xlink:label="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Allowance, Deferred Tax Asset, Increase (Decrease), Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:to="lab_us-gaap_ValuationAllowanceDeferredTaxAssetChangeInAmount" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member_9d16a5a3-9865-4c08-95bf-c7d594135ae0_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2013</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Accident Year 2013 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2013Member" 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"/>
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    <link:label id="lab_us-gaap_DiscontinuedOperationsHeldforsaleMember_681fc2fa-37b3-4c18-b39e-9f96833de249_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>
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    <link:label id="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable_9ebd6652-c0f7-4eba-8462-ed2d99937aa4_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfSubsidiaryOrEquityMethodInvesteeTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee, Sale of Stock [Table]</link:label>
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    <link:label id="lab_us-gaap_DebtInstrumentRedemptionPricePercentage_322916dd-5a45-4c8e-8143-778f66254190_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>
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    <link:label id="lab_us-gaap_ProceedsFromSaleOfAvailableForSaleSecuritiesDebt_de91aac4-172b-40b1-9873-19531fea2897_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</link:label>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsOther_c5f0dc8a-8d1a-4243-b66a-2d12121260cd_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>
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    <link:label id="lab_kg_CommonSharesHeldBySubsidiaryInExchangeForPreferenceShares_fbd2e0f3-f8fe-4e2d-b1a0-9c33c22f30df_negatedTerseLabel_en-US" xlink:label="lab_kg_CommonSharesHeldBySubsidiaryInExchangeForPreferenceShares" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Common shares held by Maiden Reinsurance (in shares)</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEquityMethodInvestmentsLineItems_88910b05-9fde-4308-8e36-6d2c6f78f638_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>
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    <link:label id="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceivedAbstract_019cbc5c-0cfe-782a-b4a9-7a1b139e3c43_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceivedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasicAbstract_375a63ec-ee77-474e-ba9c-e3812e40b23b_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>
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    <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_us-gaap_PropertyPlantAndEquipmentLineItems_7367b93a-b655-4690-bd72-9574a50b03f1_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentLineItems_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentIncomeAndGainLossOnInvestmentsNet_a914235c-2941-433e-9a4e-0f47130994cf_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-20251231.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_kg_OtherCountriesMember_14f73681-eb20-40ea-a81e-68a8d128a7a2_terseLabel_en-US" xlink:label="lab_kg_OtherCountriesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other (predominantly Europe)</link:label>
    <link:label id="lab_kg_OtherCountriesMember_label_en-US" xlink:label="lab_kg_OtherCountriesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Countries [Member]</link:label>
    <link:label id="lab_kg_OtherCountriesMember_documentation_en-US" xlink:label="lab_kg_OtherCountriesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Countries [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherCountriesMember" xlink:href="kg-20251231.xsd#kg_OtherCountriesMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherCountriesMember" xlink:to="lab_kg_OtherCountriesMember" xlink:type="arc" order="1"/>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_NonRule10b51ArrAdoptedFlag" xlink:to="lab_ecd_NonRule10b51ArrAdoptedFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVenture3Member_59ab2159-553c-4aa2-a41c-45597c7ffa7b_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-20251231.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_us-gaap_NumberOfReportableSegments_54fe8f23-d091-4d83-a493-3b2121dbb73f_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 reportable 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_ea371300-64d5-4beb-be9c-a0c5f17e090e_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">Principal repayment</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_kg_GLSToADCMember_019b02a5-3db2-7166-8051-8103c2caeda4_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-20251231.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_kg_NumberOfDirectorsSelectedByAffiliate_ff7ac563-3a26-4b5e-8596-1106046fc1d6_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-20251231.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_us-gaap_PolicyholderBenefitsAndClaimsIncurredNet_01f44535-541d-423a-beef-dbf64236d50c_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_4381b3cd-7410-4e53-96ab-2295837e77ae_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_c5298053-d9d1-43c5-a08d-d36fcbce8d19_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_92c8adfc-619d-46a1-864b-e23f8d9ee09e_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 loss adjustment expenses</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_kg_InvestmentOwnershipAtMergerClosingMember_019b0161-beb8-7ad8-9496-a88a4eb483e9_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, At Merger Closing</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-20251231.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_dei_EntityAddressCountry_5ce48d59-c90c-443e-a0fc-97adf8635a13_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_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic_66370c73-1c5b-4f9c-8c2e-0fa1e24453e4_terseLabel_en-US" xlink:label="lab_us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount of loss from discontinued operations allocated to participating common shareholders, basic</link:label>
    <link:label id="lab_us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic_label_en-US" xlink:label="lab_us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Net Income (Loss) from Discontinued Operations Available to Common Shareholders, Basic</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:to="lab_us-gaap_NetIncomeLossFromDiscontinuedOperationsAvailableToCommonShareholdersBasic" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_b8b72ead-05cc-4c20-a266-c30a16ef398a_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_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage_24bae640-c30d-4b31-adb2-ef90f8d88b41_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-20251231.xsd#kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:to="lab_kg_AssetsFairValueDisclosureValuedbyThirdPartyPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage_df22cf11-2adc-4750-9d10-6bcf9f878b28_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceAssetsAndLiabilitiesRetrocededPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">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-20251231.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_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"/>
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    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_b496469c-72fb-46b2-b006-3ce2c9e4c54c_terseLabel_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Defined contribution plans expense</link:label>
    <link:label id="lab_us-gaap_DefinedContributionPlanCostRecognized_label_en-US" xlink:label="lab_us-gaap_DefinedContributionPlanCostRecognized" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Defined Contribution Plan, Cost</link:label>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityDomain_9781772b-e760-480b-b59f-2aa86afab282_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 Jurisdiction [Domain]</link:label>
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    <link:label id="lab_us-gaap_PaymentsOfDividendsCommonStock_369d9571-ef8b-4713-91a2-0cd897d1e1d4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Dividends paid &#8211; Kestrel equityholders</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsOfDividendsCommonStock" xlink:to="lab_us-gaap_PaymentsOfDividendsCommonStock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentAnnualReport_c6520808-e55e-4fa3-9341-bd82eaa2765c_terseLabel_en-US" xlink:label="lab_dei_DocumentAnnualReport" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Annual Report</link:label>
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    <link:label id="lab_kg_NumberOfRemainingRetroactiveReinsuranceAgreements_019c0909-0f26-7a30-902e-e28fe87c381e_terseLabel_en-US" xlink:label="lab_kg_NumberOfRemainingRetroactiveReinsuranceAgreements" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of remaining retroactive reinsurance contracts</link:label>
    <link:label id="lab_kg_NumberOfRemainingRetroactiveReinsuranceAgreements_label_en-US" xlink:label="lab_kg_NumberOfRemainingRetroactiveReinsuranceAgreements" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Number Of Remaining Retroactive Reinsurance Agreements</link:label>
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    <link:label id="lab_us-gaap_LossContingencyEstimatedRecoveryFromThirdParty_019b58d9-c4bb-7708-a95c-1063d6748057_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingencyEstimatedRecoveryFromThirdParty" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimated recovery from third party</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingencyEstimatedRecoveryFromThirdParty" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingencyEstimatedRecoveryFromThirdParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingencyEstimatedRecoveryFromThirdParty" xlink:to="lab_us-gaap_LossContingencyEstimatedRecoveryFromThirdParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithoutSingleMaturityDateAmortizedCost_e10c70b8-abab-46bd-a5ae-ea5fa4de22bb_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>
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    <link:label id="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery, Explanation of Impracticability</link:label>
    <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:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:to="lab_ecd_ForgoneRecoveryExplanationOfImpracticabilityTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_MinorityInterestOwnershipPercentageByNoncontrollingOwners_ade71262-ef52-46d3-90ec-12c5da45b738_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">Noncontrolling interest, ownership percentage</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"/>
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    <link:label id="lab_kg_SegmentConcentrationRiskMember_3d104948-0562-4dd5-8c8f-00bd42da66f5_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>
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    <link:label id="lab_dei_EntityInteractiveDataCurrent_776483ba-c82c-4522-b7fd-f08684496ebc_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>
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    <link:label id="lab_kg_EarnOutLiabilityPolicyTextBlock_cdbddbf6-021a-48d4-8e98-ef17971b74af_terseLabel_en-US" xlink:label="lab_kg_EarnOutLiabilityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earn Out Liability</link:label>
    <link:label id="lab_kg_EarnOutLiabilityPolicyTextBlock_label_en-US" xlink:label="lab_kg_EarnOutLiabilityPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earn Out Liability [Policy Text Block]</link:label>
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    <link:label id="lab_kg_InvestmentManagementFeesMember_3964f5d2-2ba8-4708-98c9-01ee692ac70a_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>
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    <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-20251231.xsd#kg_InvestmentManagementFeesMember"/>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1_f4ed9d39-0c22-43f7-9d5d-bfa0140bdbb5_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsExercisableIntrinsicValue1" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total exercisable, Aggregate Intrinsic Value</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards_60341d82-75a0-4ecd-bb9a-afced97751fc_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating losses</link:label>
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    <link:label id="lab_kg_CommonStockNumberOfVotesPerShare_a4ab0676-7eca-4a4d-bef3-fab7b8c8a9e7_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>
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    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis_3c8a9dc6-12e5-40a7-9818-3073c09bc883_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Axis]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentByTypeAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentByTypeAxis"/>
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    <link:label id="lab_kg_MaidenLfMember_documentation_en-US" xlink:label="lab_kg_MaidenLfMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maiden LF [Member]</link:label>
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    <link:label id="lab_kg_OtherComprehensiveIncomeLossInvestmentsAdjustmentNetOfTaxPortionAttributableToParent_b92c5845-8c1c-4dcc-ab23-36134b372539_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 gains on investment</link:label>
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    <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>
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    <link:label id="lab_us-gaap_Revenues_052fa6d2-6c83-4924-b803-279d18f728a8_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>
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    <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>
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    <link:label id="lab_kg_InvestmentOwnership5PercentMember_019b0161-beb8-78ef-918f-add0355ebb04_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 Percent</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember_0dc2e0bc-bc94-487e-9a9d-cf7585fece8e_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAwardTrancheOneMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting on First Anniversary of Grant Date</link:label>
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    <link:label id="lab_us-gaap_StatutoryAccountingPracticesStatutoryNetIncomeAmount_e02eea4d-ca92-442c-84de-78d78ff5d543_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesStatutoryNetIncomeAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Net Income (Loss)</link:label>
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    <link:label id="lab_us-gaap_PremiumsWrittenNet_419ff085-ed5d-4e4e-841b-82eb5d93f494_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_a36e3a38-5012-4163-b85c-b8026ce5d2f3_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_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_AssetsHeldByInsuranceRegulators_b2037420-884d-4305-975c-71c85b3a4a8b_terseLabel_en-US" xlink:label="lab_us-gaap_AssetsHeldByInsuranceRegulators" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory assets</link:label>
    <link:label id="lab_us-gaap_AssetsHeldByInsuranceRegulators_label_en-US" xlink:label="lab_us-gaap_AssetsHeldByInsuranceRegulators" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Assets Held by Insurance Regulators</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AssetsHeldByInsuranceRegulators" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AssetsHeldByInsuranceRegulators"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_AssetsHeldByInsuranceRegulators" xlink:to="lab_us-gaap_AssetsHeldByInsuranceRegulators" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts_fe39a7ee-b1af-49e5-9f16-88bf57c6344a_verboseLabel_en-US" xlink:label="lab_us-gaap_PremiumsReceivableAllowanceForDoubtfulAccounts" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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_d6145242-eee4-4e9e-9ca6-b41c6368576c_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_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_7dc4b566-dea0-46d0-b6f7-a55589e478e9_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Federal tax rate</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation, at Federal Statutory Income Tax Rate, Percent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationAtFederalStatutoryIncomeTaxRate" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree_019cd080-89bc-7783-9862-eb4aa0eb20ac_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearThree" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2028</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_VestingDomain_916236a7-8e91-4146-8d2b-be577e67e847_terseLabel_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:label id="lab_us-gaap_VestingDomain_label_en-US" xlink:label="lab_us-gaap_VestingDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingDomain" xlink:to="lab_us-gaap_VestingDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LeahKarfunkelMember_019b0161-beb8-754c-855c-dee64e7c7cbf_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-20251231.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_DisposalGroupIncludingDiscontinuedOperationCashAndCashEquivalents_77a47094-b61e-43d7-8cea-c69297521fce_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_us-gaap_DeferredTaxAssetsNetAbstract_13aee7ae-f4bd-4908-bea4-1ea5a89e715a_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets:</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsNetAbstract_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsNetAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Net [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsNetAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsNetAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsNetAbstract" xlink:to="lab_us-gaap_DeferredTaxAssetsNetAbstract" 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_4e6622ba-2682-4196-9018-42123fad65b9_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_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_eea474cb-c624-4e04-bd05-de0abe9961ef_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_us-gaap_AccumulatedOtherComprehensiveIncomeMember_86e3f32f-2ba6-4d0c-b044-3cc4d9a5022b_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_7cfdff37-5d87-4046-9baa-4152365915d5_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_715e5453-16eb-4b66-8264-efa06b939eea_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_1c681b00-73e9-464d-b2dd-657132c5e817_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_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_c09017ea-35f3-45e6-8b2f-f6ae57ceb54d_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Issuance of common shares due to the Combination (in shares)</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Shares, Conversion of Convertible Securities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:to="lab_us-gaap_StockIssuedDuringPeriodSharesConversionOfConvertibleSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_ac2ddd70-8d95-4ab3-8e56-8ff4aaf5f5ce_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: 2025 - $1,740)</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_77f09d6e-cb8f-4463-91c0-c1eaadeb4388_netLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Reinsurance recoverable on unpaid losses</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableForUnpaidClaimsAndClaimsAdjustments_47b0218c-c5e2-4151-abdd-31a54403aa00_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">Impact of LPT/ADC</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"/>
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    <link:label id="lab_kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued_e8235d5d-a49d-421e-874d-bc0013edd5b2_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-20251231.xsd#kg_BusinessCombinationContingentConsiderationSharesIssuedOrToBeIssued"/>
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    <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_srt_OwnershipAxis_fe96cc52-67d8-4606-bedd-49a4c50126f3_terseLabel_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:label id="lab_srt_OwnershipAxis_label_en-US" xlink:label="lab_srt_OwnershipAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Ownership [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_OwnershipAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_OwnershipAxis"/>
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    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments_1cd18565-e966-43c9-9529-8fbad1060d49_terseLabel_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Proceeds from sale and redemption of other investments</link:label>
    <link:label id="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments_label_en-US" xlink:label="lab_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Proceeds from Sale and Maturity of Other Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ProceedsFromSaleAndMaturityOfOtherInvestments"/>
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    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod_019c323a-0516-706f-8659-3964d52f8591_terseLabel_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards replaced (in shares)</link:label>
    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod_label_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod" 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, Equity Instruments Other Than Options, Replaced In Period</link:label>
    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod_documentation_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Equity Instruments Other Than Options, Replaced In Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod" xlink:href="kg-20251231.xsd#kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod" xlink:to="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_7946e94b-a405-4079-b99c-90388bd28cc6_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Statement, Balance Sheet and Additional Disclosures by Disposal Groups, Including Discontinued Operations [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesPercentofTotalFairValue_4825bd48-2525-4765-a051-7d20b56eb8c6_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>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FixedMaturitiesPercentofTotalFairValue" xlink:href="kg-20251231.xsd#kg_FixedMaturitiesPercentofTotalFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesPercentofTotalFairValue" xlink:to="lab_kg_FixedMaturitiesPercentofTotalFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_AwardGrantDateFairValue_terseLabel_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair Value as of Grant Date</link:label>
    <link:label id="lab_ecd_AwardGrantDateFairValue_label_en-US" xlink:label="lab_ecd_AwardGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_AwardGrantDateFairValue" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_AwardGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_AwardGrantDateFairValue" xlink:to="lab_ecd_AwardGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_01b5a14d-993a-48ed-ae3f-5774566cd12a_verboseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Equity securities, at fair value, cost</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_9817e30c-ca29-4f8d-92ef-f19f80bd6709_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cost</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCost_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Cost</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiCost" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiCost"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiCost" xlink:to="lab_us-gaap_EquitySecuritiesFvNiCost" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedCashAndInvestmentsLineItems_9baa8aa4-ad11-400d-8403-498a5863ac7e_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-20251231.xsd#kg_RestrictedCashAndInvestmentsLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RestrictedCashAndInvestmentsLineItems" xlink:to="lab_kg_RestrictedCashAndInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AmtrustFinancialServicesIncMember_6d5e7112-b459-4541-8f9c-d7c854fd81c1_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_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-20251231.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_OperatingLossCarryforwards_616bc032-1d82-48a1-8d55-25633418fb20_terseLabel_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Operating Loss carryforwards</link:label>
    <link:label id="lab_us-gaap_OperatingLossCarryforwards_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwards" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwards" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwards"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OperatingLossCarryforwards" xlink:to="lab_us-gaap_OperatingLossCarryforwards" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_53bb6df5-aca5-4935-a2e2-bfd58aeaaa1e_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" 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_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" 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 Balances Receivable, Net</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" 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 Balances Receivable, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet" xlink:href="kg-20251231.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceBalancesReceivableNet"/>
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    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_21134b8e-924d-4327-b17e-96ec9dfcee10_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Issuances of Senior Notes Outstanding</link:label>
    <link:label id="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Long-Term Debt Instruments [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfDebtInstrumentsTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:to="lab_us-gaap_ScheduleOfDebtInstrumentsTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_6ed38c50-4cba-49cf-8628-b4cf70f0ed44_verboseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Awards granted (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" 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, Equity Instruments Other than Options, Grants in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommonStockShareholderVotingPowerPercentage_fc77ee6e-7daa-49ec-8701-8c84a929ea14_terseLabel_en-US" xlink:label="lab_kg_CommonStockShareholderVotingPowerPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholder voting power, percentage</link:label>
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    <link:label id="lab_kg_CommonStockShareholderVotingPowerPercentage_documentation_en-US" xlink:label="lab_kg_CommonStockShareholderVotingPowerPercentage" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Common Stock, Shareholder Voting Power, Percentage</link:label>
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    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_a5e9ea20-7d28-4adb-8130-628cc5fdaa7e_terseLabel_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title and Position [Domain]</link:label>
    <link:label id="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain_label_en-US" xlink:label="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TitleOfIndividualWithRelationshipToEntityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:to="lab_srt_TitleOfIndividualWithRelationshipToEntityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized_f824080b-ffeb-4670-894f-c5e82f373cbb_terseLabel_en-US" xlink:label="lab_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total unrecognized compensation cost</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EmployeeServiceShareBasedCompensationNonvestedAwardsTotalCompensationCostNotYetRecognized"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_d4eeb93a-3814-44a6-a5ea-eb57d215d891_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Awards forfeited (in shares)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" 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, Equity Instruments Other than Options, Forfeited in Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_a3ab4279-2480-4d6f-ad55-53cd07976909_terseLabel_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:label id="lab_us-gaap_RelatedPartyTransactionLineItems_label_en-US" xlink:label="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RelatedPartyTransactionLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RelatedPartyTransactionLineItems" xlink:to="lab_us-gaap_RelatedPartyTransactionLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_e655b5cf-0a1d-4a4d-84bc-e3d6a03ee49d_verboseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Expected credit losses on acquired recoverables under the Combination</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_7f33f898-8b04-4419-832e-29e67a1d5507_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" 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 on acquired assets</link:label>
    <link:label id="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal_label_en-US" xlink:label="lab_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Recoverable, Credit Loss Expense (Reversal)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceRecoverableCreditLossExpenseReversal"/>
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    <link:label id="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock_a44779a4-93d7-42eb-8a6b-374a5bb3f6cf_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisValuationTechniquesTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Significant Unobservable Inputs for Determining Fair Value of Other Investments</link:label>
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    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_terseLabel_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote</link:label>
    <link:label id="lab_ecd_ChangedPeerGroupFnTextBlock_label_en-US" xlink:label="lab_ecd_ChangedPeerGroupFnTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Changed Peer Group, Footnote [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ChangedPeerGroupFnTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ChangedPeerGroupFnTextBlock"/>
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    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member_76fe68df-75db-46f0-942b-7dfc9299044d_terseLabel_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2021</link:label>
    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member_label_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contract, Accident Year 2021 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortDurationInsuranceContractAccidentYear2021Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member" xlink:to="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2021Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_4e0a2900-6f0c-47f8-8772-f492d7fb312f_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">2027</link:label>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
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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>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_c86f8d98-0e25-446a-bcbd-896534417bba_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Outstanding, Weighted Average Remaining Contractual Term</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" 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, Options, Outstanding, Weighted Average Remaining Contractual Term</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardOptionsOutstandingWeightedAverageRemainingContractualTerm2"/>
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    <link:label id="lab_us-gaap_AccruedInvestmentIncomeReceivable_3c6c4e63-2239-49e5-9a85-663a729de18b_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>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2009Member_88b5bf0f-1120-4577-9d75-873b4a657deb_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2009Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2009</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2009Member_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2009Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Accident Year 2009 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsAccidentYear2009Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsAccidentYear2009Member"/>
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    <link:label id="lab_us-gaap_InvestmentTypeAxis_9af3e149-ec22-4648-96a2-ff9754aff213_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>
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    <link:label id="lab_us-gaap_Investments_f4c9773d-3b46-4fc9-a5fb-3dcfbdfee7d0_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>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityLineItems_3760a39b-10b0-45d0-8114-427e831fdd24_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">US Treaty business ceded to Cavello</link:label>
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    <link:label id="lab_us-gaap_LettersOfCreditOutstandingAmount_fe6ac30b-573c-48fb-ae0f-65e857e6c99f_terseLabel_en-US" xlink:label="lab_us-gaap_LettersOfCreditOutstandingAmount" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Letters of credit outstanding</link:label>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTableTextBlock_072ea2ae-ccec-4ebd-895b-b9c025818074_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Reconciliation of Claims Development to Liability</link:label>
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    <link:label id="lab_us-gaap_FeeIncome_dae7c200-3445-46b1-bbe9-02b9a9ff9122_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, net</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_9db891a1-08ed-419e-b894-3627deba174c_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">2026</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_PaymentsForProceedsFromLoansReceivable_44a4cc59-070b-4990-ae35-195003e09ac7_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForProceedsFromLoansReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" 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"/>
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    <link:label id="lab_us-gaap_ReinsuranceReceivablesIncurredButNotReportedClaims_ae1cc47a-6fa6-4326-98fb-45ca5a5c12b7_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"/>
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    <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_us-gaap_LeaseholdImprovementsMember_c0e3de37-587f-4dcf-b7e3-2413d1635d51_terseLabel_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Leasehold improvements</link:label>
    <link:label id="lab_us-gaap_LeaseholdImprovementsMember_label_en-US" xlink:label="lab_us-gaap_LeaseholdImprovementsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Leasehold Improvements [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LeaseholdImprovementsMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LeaseholdImprovementsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LeaseholdImprovementsMember" xlink:to="lab_us-gaap_LeaseholdImprovementsMember" 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>
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    <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_us-gaap_DebtInstrumentNameDomain_eed74909-97a3-4c0e-9ba2-6f7a1a820d50_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentNameDomain" xlink:to="lab_us-gaap_DebtInstrumentNameDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense_f6dac033-5714-435a-aa05-903117bb1627_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule for Reserve for Loss and LAE and Schedule of Prior Period Development Experienced</link:label>
    <link:label id="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense_label_en-US" xlink:label="lab_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Liability for Unpaid Claims and Claims Adjustment Expense [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfLiabilityForUnpaidClaimsAndClaimsAdjustmentExpense"/>
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    <link:label id="lab_ecd_RecoveryOfErrCompDisclosureLineItems_label_en-US" xlink:label="lab_ecd_RecoveryOfErrCompDisclosureLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Recovery of Erroneously Awarded Compensation Disclosure [Line Items]</link:label>
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    <link:label id="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember_a3bf7c75-cba4-4663-9c39-400b90112388_terseLabel_en-US" xlink:label="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" 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_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:to="lab_us-gaap_EstimateOfFairValueFairValueDisclosureMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember_019cded9-c842-77bd-b997-b58a42a5ca8d_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>
    <link:label id="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember_label_en-US" xlink:label="lab_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Valuation Technique, Price of Comparable Business [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_GoodwillImpairmentLossMethodForFairValueDeterminationPriceOfComparableBusinessMember"/>
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    <link:label id="lab_us-gaap_ScheduleOfInvestmentsLineItems_57c3537e-f749-4ac9-a546-13f32bc30f3d_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfInvestmentsLineItems" xlink:to="lab_us-gaap_ScheduleOfInvestmentsLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_ecd_MnpiDiscTimedForCompValFlag_terseLabel_en-US" xlink:label="lab_ecd_MnpiDiscTimedForCompValFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">MNPI Disclosure Timed for Compensation Value</link:label>
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    <link:label id="lab_kg_FixedMaturitiesAmortizedCostBasis_50998e4e-9c87-4877-be68-693fee3c025b_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>
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    <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-20251231.xsd#kg_FixedMaturitiesAmortizedCostBasis"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_6bf79b36-d047-4c1c-9c37-3992c073eb55_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>
    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost_label_en-US" xlink:label="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterOneThroughFiveYearsAmortizedCost" 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 One Through Five</link:label>
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    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential_019ca05f-73c4-724b-906f-1d1c62e36ba0_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationForeignIncomeTaxRateDifferential" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign tax rate</link:label>
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    <link:label id="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain_documentation_en-US" xlink:label="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Realized And Unrealized Gain</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:href="kg-20251231.xsd#kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:to="lab_kg_EquitySecuritiesFVNIRealizedAndUnrealizedGain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt_db4f4063-f672-4aa8-b576-1a1c62f9e166_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-20251231.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLongTermDebt"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsIncurredClaimsAndAllocatedClaimAdjustmentExpenseNet_8930c2f6-f6df-4500-94d9-10c2fd18c4d5_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsIncurredClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Incurred loss and LAE, net of reinsurance</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsIncurredClaimsAndAllocatedClaimAdjustmentExpenseNet_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsIncurredClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Incurred Claims and Allocated Claim Adjustment Expense, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsIncurredClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsIncurredClaimsAndAllocatedClaimAdjustmentExpenseNet"/>
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    <link:label id="lab_kg_TreasuryStockSharesIssuedToSubsidiary_0488d166-ce96-4885-86e2-b94b411b6c7d_negatedTerseLabel_en-US" xlink:label="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Shares issued to Maiden Reinsurance</link:label>
    <link:label id="lab_kg_TreasuryStockSharesIssuedToSubsidiary_label_en-US" xlink:label="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares Issued to Subsidiary</link:label>
    <link:label id="lab_kg_TreasuryStockSharesIssuedToSubsidiary_documentation_en-US" xlink:label="lab_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Treasury Stock, Shares Issued to Subsidiary</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_TreasuryStockSharesIssuedToSubsidiary" xlink:href="kg-20251231.xsd#kg_TreasuryStockSharesIssuedToSubsidiary"/>
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    <link:label id="lab_kg_ValueOfBusinessAcquiredMember_019cd30c-eb7a-7bc6-a9a9-09736ce2a566_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_019cd07f-127b-74f9-9026-710390097d74_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-20251231.xsd#kg_ValueOfBusinessAcquiredMember"/>
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    <link:label id="lab_us-gaap_RevenuesAbstract_e3ce6226-135f-4c80-a902-a20a2f749caa_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RevenuesAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RevenuesAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RevenuesAbstract" xlink:to="lab_us-gaap_RevenuesAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentMilestoneTypeAxis_019b0161-beb8-722b-b8b1-c528a8f013bc_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-20251231.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_dei_DocumentsIncorporatedByReferenceTextBlock_1c75db9f-c134-4085-bec1-72de7acac646_terseLabel_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference</link:label>
    <link:label id="lab_dei_DocumentsIncorporatedByReferenceTextBlock_label_en-US" xlink:label="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Documents Incorporated by Reference [Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentsIncorporatedByReferenceTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:to="lab_dei_DocumentsIncorporatedByReferenceTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignGovernmentDebtMember_de169132-cf49-4c73-b47f-95db58fa47d5_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_a887283d-f78e-4e02-8e93-e8f6f36fe6cd_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignGovernmentDebtMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignGovernmentDebtMember"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsAmortizedCost_c82d9bcd-495a-4ef5-b774-56da17b030cc_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_307d9805-207f-4466-a081-c675876e8434_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_d34649d2-912a-4a6d-a8fe-5336a34522f2_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_RestrictedCashAndInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_RestrictedCashAndInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_RestrictedCashAndInvestments" xlink:to="lab_us-gaap_RestrictedCashAndInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock_469a8e85-c857-4d5e-9c8c-3608e2efa291_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Fair Value of Restricted Assets</link:label>
    <link:label id="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Financial Instruments Owned and Pledged as Collateral [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfFinancialInstrumentsOwnedAndPledgedAsCollateralTextBlock"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable_50587704-a537-478c-b486-2e808dbd8752_negatedLabel_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accrued investment income</link:label>
    <link:label id="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable_label_en-US" xlink:label="lab_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Increase (Decrease) in Accrued Investment Income Receivable</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncreaseDecreaseInAccruedInvestmentIncomeReceivable"/>
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    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_da5be806-f178-4ae3-9fb2-b2847d9ab15c_verboseLabel_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Accumulated other comprehensive income</link:label>
    <link:label id="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax_label_en-US" xlink:label="lab_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Accumulated Other Comprehensive Income (Loss), Net of Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_AccumulatedOtherComprehensiveIncomeLossNetOfTax"/>
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    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_54d864be-34e1-4e31-af2a-0bf62f464038_terseLabel_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:label id="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_label_en-US" xlink:label="lab_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Financial Instruments [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain"/>
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    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_0907a1f2-c579-49e4-b460-94fbe8e97ef1_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Deferred tax liabilities</link:label>
    <link:label id="lab_us-gaap_DeferredIncomeTaxLiabilities_label_en-US" xlink:label="lab_us-gaap_DeferredIncomeTaxLiabilities" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Gross</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxLiabilities" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxLiabilities"/>
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    <link:label id="lab_kg_RelatedPartyTransactionPercentOfCedingCommissionPayablePeriodIncreaseDecrease_2d603f33-1107-4c94-b307-e11745d4633e_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>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_aa6149ae-74c4-475b-b696-ec51bd472052_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_kg_SummitFinancialServicesInc.Member_019c8f29-6e9d-73c2-b15e-9e87e2254d4d_terseLabel_en-US" xlink:label="lab_kg_SummitFinancialServicesInc.Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summit Financial Services, Inc.</link:label>
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    <link:label id="lab_us-gaap_ReconciliationOfAssetsFromSegmentToConsolidatedTable_e7f300be-f188-4a14-9baf-fbac0cdb9379_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>
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    <link:label id="lab_kg_PrivateCreditLendingMember_ee1f7f9b-2a9d-4519-b6b7-515dd619b902_terseLabel_en-US" xlink:label="lab_kg_PrivateCreditLendingMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Private credit funds</link:label>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member_196daa06-99e0-46b1-8cc6-0540e62af305_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1Member" 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_us-gaap_LossContingenciesTable_label_en-US" xlink:label="lab_us-gaap_LossContingenciesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Table]</link:label>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverablesOnUnpaidLossesGross_ba7fc4f1-6217-46f9-8504-a97c47f63eaf_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 recoverable on unpaid gross</link:label>
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    <link:label id="lab_us-gaap_CededCreditRiskReinsurerDomain_7242a6c8-a40a-47eb-8996-8dc906edfeb5_terseLabel_en-US" xlink:label="lab_us-gaap_CededCreditRiskReinsurerDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurer, Name [Domain]</link:label>
    <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>
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    <link:label id="lab_us-gaap_AssumedPremiumsEarned_02beec9a-4c70-4aca-b13f-c6bd89469eeb_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>
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    <link:label id="lab_srt_RangeAxis_21b28efc-edb3-4d14-8160-f289be4361ef_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>
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    <link:loc xlink:type="locator" xlink:label="loc_srt_RangeAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_RangeAxis"/>
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    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesDomain_96a3e716-0fdf-483c-af07-9dece26db5db_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>
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    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsReplacedInPeriod_019c3245-1bee-74b0-9693-604949f9db96_terseLabel_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsReplacedInPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options replaced (in shares)</link:label>
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    <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>
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    <link:label id="lab_kg_FundsWithheldArrangementMember_45b191a3-d764-4038-b096-f8274b218981_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>
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    <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>
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    <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>
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    <link:label id="lab_us-gaap_NetIncomeLossAvailableToCommonStockholdersBasic_92b50b60-4580-46d3-b6b1-4ea3d2b1b55e_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 income (loss) attributable to Kestrel common shareholders, basic</link:label>
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    <link:label id="lab_kg_DirectLendingEntitiesMember_8a6fd512-47ef-41fe-93c6-35a3cf99b2b0_terseLabel_en-US" xlink:label="lab_kg_DirectLendingEntitiesMember" 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_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-20251231.xsd#kg_DirectLendingEntitiesMember"/>
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    <link:label id="lab_us-gaap_OperatingExpenses_95f32f28-a847-4724-944a-e71b838dd3a0_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_15e848ad-314d-4326-909a-d2e3d2cd2d3e_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_4f53ae71-ed35-44ff-9974-f24bcdf23c56_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_us-gaap_FairValueInputsLevel1Member_225546fc-c479-4662-bd2c-726c7ed97b28_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"/>
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    <link:label id="lab_srt_StandardPoorsAAARatingMember_6da256db-d2a3-474d-b5a0-1b419403536c_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_d8f4b277-1e1d-499f-bc56-bb96058c317c_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">Related Party Transaction [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_3c5f2640-822f-413e-b7b5-44061535e38f_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 earnings (loss) per share available to Kestrel common 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"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesAfterFiveThroughTenYearsFairValue_f5b8d3a9-aee9-46ec-8f9b-363c4b250e12_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"/>
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    <link:label id="lab_us-gaap_ReinsuranceAccountingPolicy_65222932-2889-4dde-97fc-7364886977af_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceAccountingPolicy" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance and Retroactive Reinsurance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceAccountingPolicy_label_en-US" xlink:label="lab_us-gaap_ReinsuranceAccountingPolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Accounting Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ReinsuranceAccountingPolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ReinsuranceAccountingPolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ReinsuranceAccountingPolicy" xlink:to="lab_us-gaap_ReinsuranceAccountingPolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities_e1f61bcc-2b97-4c58-ba35-0495f402e7b3_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-20251231.xsd#kg_DisposalGroupIncludingDiscontinuedOperationDebtSecurities"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonShares_9da39c27-19a0-4854-9fed-e64c87bc7331_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, at cost (in shares)</link:label>
    <link:label id="lab_us-gaap_TreasuryStockCommonShares_fd023ef9-efe8-47ae-9fd7-f59e80470308_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 (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_RealizedAndUnrealizedLossOnInvestments_f388041f-8e2a-4d90-b6f7-4af037126c1c_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>
    <link:label id="lab_kg_RealizedAndUnrealizedLossOnInvestments_label_en-US" xlink:label="lab_kg_RealizedAndUnrealizedLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Realized And Unrealized Loss On Investments</link:label>
    <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-20251231.xsd#kg_RealizedAndUnrealizedLossOnInvestments"/>
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    <link:label id="lab_srt_ConsolidationItemsDomain_b7a30545-98e0-410c-8b25-4144412944d8_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_019b094e-b3f4-77df-bb31-46dd3507339c_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"/>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member_019caf7d-a33b-7d11-9b4d-ef998a85c89e_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>
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    <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-20251231.xsd#kg_PrivatelyHeldEquityInvestmentsInPreferredStock3Member"/>
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    <link:label id="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax_76b16be9-8f2e-4622-a33e-05c5666c5ed4_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromDiscontinuedOperationsNetOfTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Add: Net loss from discontinued operations</link:label>
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    <link:label id="lab_dei_AuditorLocation_81dfe5d4-66c0-4b9d-bb3b-68652daff123_terseLabel_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:label id="lab_dei_AuditorLocation_label_en-US" xlink:label="lab_dei_AuditorLocation" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Location</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorLocation" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorLocation"/>
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    <link:label id="lab_kg_LegacyReinsuranceSegmentMember_c60477b0-3e34-4c79-ae2d-1438a60d04f7_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_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>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LegacyReinsuranceSegmentMember" xlink:href="kg-20251231.xsd#kg_LegacyReinsuranceSegmentMember"/>
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    <link:label id="lab_kg_RelatedPartyTransactionMaximumLimitOfLiabilityAttaching_4adc6fb4-1957-45fd-a65d-5ce831c175e7_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 (in EUR)</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-20251231.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_us-gaap_CededCreditRiskAxis_96a6165d-0071-4518-b59f-1f9a5ee550f6_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_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock_6b687dd0-8b78-4ff4-97fa-d6b3524bfb3a_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Incurred Losses And LAE And Cumulative Paid Losses And LAE</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Claims Development [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts_55607320-e57b-4a2b-bc7e-ef212502c71f_terseLabel_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Number of short duration insurance contracts</link:label>
    <link:label id="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts_label_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short Duration Insurance Contracts, Number Of Major Contracts</link:label>
    <link:label id="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts_documentation_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Short Duration Insurance Contracts, Number Of Major Contracts</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShortDurationInsuranceContractsNumberOfMajorContracts" xlink:href="kg-20251231.xsd#kg_ShortDurationInsuranceContractsNumberOfMajorContracts"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShortDurationInsuranceContractsNumberOfMajorContracts" xlink:to="lab_kg_ShortDurationInsuranceContractsNumberOfMajorContracts" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverables_dd201e3c-88b5-4030-b37d-be641bebc898_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_3e523a64-15e4-43b2-b3af-52ddadbb3c8c_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, December 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_d64f56e2-9f3c-4806-b586-58b512670f32_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_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_2a84f6f6-fde2-47ee-a7f6-aaef87bc169e_negatedLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Accrued expenses and other liabilities</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_label_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" 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 Expenses and Other Liabilities</link:label>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities_documentation_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" 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 Expenses and Other Liabilities</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:href="kg-20251231.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedAccruedExpensesAndOtherLiabilities" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_019cbc5c-0cfe-7b29-8fb9-d9c83f9fa1de_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total income taxes paid</link:label>
    <link:label id="lab_us-gaap_IncomeTaxesPaidNet_label_en-US" xlink:label="lab_us-gaap_IncomeTaxesPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Taxes Paid, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxesPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxesPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxesPaidNet" xlink:to="lab_us-gaap_IncomeTaxesPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateBondSecuritiesMember_3c06c4fb-670c-45ec-8c50-fdc7f7bc5bd9_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_019cd080-74a6-78de-86b0-1a9ea9fe4da5_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearTwo" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2027</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_us-gaap_OtherInsuranceProductLineMember_a5a355f3-1149-4609-9c8b-012c0d77c18d_terseLabel_en-US" xlink:label="lab_us-gaap_OtherInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">All other lines</link:label>
    <link:label id="lab_us-gaap_OtherInsuranceProductLineMember_label_en-US" xlink:label="lab_us-gaap_OtherInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance, Other [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherInsuranceProductLineMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherInsuranceProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherInsuranceProductLineMember" xlink:to="lab_us-gaap_OtherInsuranceProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentCarryingAmount_cfe51b3d-d686-4396-a674-4c71867de5e0_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_2d757a9b-df92-4ec1-82aa-c4eb934f7344_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_dei_EntityWellKnownSeasonedIssuer_433dca5b-2c02-47ca-82d9-415af3c3b935_terseLabel_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:label id="lab_dei_EntityWellKnownSeasonedIssuer_label_en-US" xlink:label="lab_dei_EntityWellKnownSeasonedIssuer" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Well-known Seasoned Issuer</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityWellKnownSeasonedIssuer" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityWellKnownSeasonedIssuer"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityWellKnownSeasonedIssuer" xlink:to="lab_dei_EntityWellKnownSeasonedIssuer" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member_bd0fbbbb-d108-4dac-a019-60a76306ad95_terseLabel_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2024</link:label>
    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member_label_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contract, Accident Year 2024 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortDurationInsuranceContractAccidentYear2024Member"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member" xlink:to="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2024Member" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember_f491b9a3-221d-403b-b081-8037965d4dc4_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">General Liability</link:label>
    <link:label id="lab_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember_label_en-US" xlink:label="lab_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Liability and Casualty Insurance Product Line [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember" xlink:to="lab_us-gaap_PropertyLiabilityAndCasualtyInsuranceSegmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentOwnedBalanceShares_019b0161-beb8-75e2-b700-fd968e208f72_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_kg_RestrictedCashAndInvestmentsTypeAxis_3f66b382-e58c-4845-b667-ae92c42f0bac_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-20251231.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_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_019cd080-a3bf-7f18-a032-19d552a13f18_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2030</link:label>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:to="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyTransactionAmountsOfTransaction_d502dad6-36c9-44c5-9b2d-8bd81c8f10db_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_kg_RealEstateInvestmentsAtFairValueMember_019b00c9-5554-7995-8739-c89c008560aa_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-20251231.xsd#kg_RealEstateInvestmentsAtFairValueMember"/>
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    <link:label id="lab_us-gaap_StockholdersEquityIncludingPortionAttributableToNoncontrollingInterestAbstract_d84a1cbf-14d4-4608-9950-37cf8accca7b_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"/>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss_af039268-10fc-4646-88b0-2de05df6565a_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains recognized for equity securities held at reporting date</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Unrealized Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiUnrealizedGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FixedIncomeSecuritiesMember_04adda98-2d39-4b7d-beb4-63a2c3da76a7_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_kg_StandardPoorsSingleaPlusSingleaAndSingleaMinusMember_d154c9c6-3239-4d3c-988b-a1d44ea6cb9d_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-20251231.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_us-gaap_OtherInvestmentsMember_1af39071-9fbf-4d64-a635-368375d124c3_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_019caf80-a9b3-7db6-845b-1c8bfbfbd67d_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_48ab7d46-b529-49d2-89d0-9fd94c4d36ce_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_PropertyPlantAndEquipmentNet_c1fd771f-09d2-4f4b-acb9-dc219d8ae2a5_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net carrying value</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_f46ef631-973d-44fb-8560-b4934b8f847b_totalLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Net carrying value</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentNet_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentNet" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsTextBlock_825420d5-2113-44c5-9ae3-3134ce4985c7_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_7f687654-6f30-4927-b7f0-e851e4cdd381_terseLabel_en-US" xlink:label="lab_us-gaap_CededPremiumsWritten" xlink:role="http://www.xbrl.org/2003/role/terseLabel" 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_dei_EntityCurrentReportingStatus_43768cdb-81c6-4d8f-bd9d-fd5b4193fc36_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_kg_GLSInsuranceMember_1d147012-5b9d-4bb5-b76e-0e03729a03a9_terseLabel_en-US" xlink:label="lab_kg_GLSInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">GLS</link:label>
    <link:label id="lab_kg_GLSInsuranceMember_label_en-US" xlink:label="lab_kg_GLSInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">GLS Insurance [Member]</link:label>
    <link:label id="lab_kg_GLSInsuranceMember_documentation_en-US" xlink:label="lab_kg_GLSInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">GLS Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_GLSInsuranceMember" xlink:href="kg-20251231.xsd#kg_GLSInsuranceMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GLSInsuranceMember" xlink:to="lab_kg_GLSInsuranceMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock2Member_019caf7d-4a3e-77a5-ad6d-5e1a462ded4a_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-20251231.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_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>
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    <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_bec0d472-e139-44bd-ad78-7786222cf62b_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_kg_RelatedPartyTransactionPremiumsAndLossesRelatedToPolicies_81b0c6f4-0a63-4d61-9052-df9938ae2001_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>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_e409d392-18dd-4930-86f9-8c2f40399ab9_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>
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    <link:label id="lab_us-gaap_ScheduleOfFairValueAssetsAndLiabilitiesMeasuredOnRecurringBasisTableTextBlock_92617247-75c6-427e-8529-feb127030ad3_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>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNi_9a74a67e-aa8b-4859-af66-8637042a73d6_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, at fair value (Cost: 2025 - $11,145)</link:label>
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    <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_us-gaap_StockIssuedDuringPeriodValueAcquisitions_861d298d-3fef-498b-aeaa-1ea45b60ed96_terseLabel_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shares issued on Combination Agreement</link:label>
    <link:label id="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions_label_en-US" xlink:label="lab_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Stock Issued During Period, Value, Acquisitions</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockIssuedDuringPeriodValueAcquisitions" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockIssuedDuringPeriodValueAcquisitions"/>
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    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNet_99277c26-5a1f-49c8-bc01-cbe7038b447d_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_c002f75d-bf3e-425a-86a5-1ab49098a608_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>
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    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_0d7fc32b-ed98-4c0f-a974-418aeb7d14b6_terseLabel_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Unrecognized tax benefits</link:label>
    <link:label id="lab_us-gaap_UnrecognizedTaxBenefits_label_en-US" xlink:label="lab_us-gaap_UnrecognizedTaxBenefits" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unrecognized Tax Benefits</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnrecognizedTaxBenefits" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnrecognizedTaxBenefits"/>
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    <link:label id="lab_kg_OtherRunOffLinesInsuranceMember_9fd6d0c4-a71c-4629-9058-2a03b4636ec5_terseLabel_en-US" xlink:label="lab_kg_OtherRunOffLinesInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other run-off lines</link:label>
    <link:label id="lab_kg_OtherRunOffLinesInsuranceMember_label_en-US" xlink:label="lab_kg_OtherRunOffLinesInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Run-off Lines Insurance [Member]</link:label>
    <link:label id="lab_kg_OtherRunOffLinesInsuranceMember_documentation_en-US" xlink:label="lab_kg_OtherRunOffLinesInsuranceMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Other Run-off Lines Insurance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_OtherRunOffLinesInsuranceMember" xlink:href="kg-20251231.xsd#kg_OtherRunOffLinesInsuranceMember"/>
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    <link:label id="lab_kg_DiscretionaryPerformanceBasedRestrictedSharesMember_1e776570-7aa8-4fdd-81bb-2db80a4c44fc_terseLabel_en-US" xlink:label="lab_kg_DiscretionaryPerformanceBasedRestrictedSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discretionary Performance-Based Restricted Shares</link:label>
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    <link:label id="lab_kg_DiscretionaryPerformanceBasedRestrictedSharesMember_documentation_en-US" xlink:label="lab_kg_DiscretionaryPerformanceBasedRestrictedSharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Discretionary Performance-Based Restricted Shares</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_DiscretionaryPerformanceBasedRestrictedSharesMember" xlink:href="kg-20251231.xsd#kg_DiscretionaryPerformanceBasedRestrictedSharesMember"/>
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    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2025Member_019c728f-b5e1-7746-b674-d53d40867bd0_terseLabel_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2025Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2025</link:label>
    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2025Member_label_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2025Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contract, Accident Year 2025 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortDurationInsuranceContractAccidentYear2025Member" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortDurationInsuranceContractAccidentYear2025Member"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFour_c9b7d813-90b1-457d-bc4e-aa69d8daf475_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFour" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 4</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFour_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFour" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Historical Claims Duration, Year Four</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFour" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFour"/>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsInvestments_00c92a0b-f604-4979-a141-2d2308ba1f97_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInvestments" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains on investments</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsInvestments_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsInvestments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Investments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsInvestments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsInvestments"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivities_de880710-82c0-4bf3-9796-3a987e858dcd_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>
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    <link:label id="lab_kg_KestrelGroupLtd.Member_bf504dcc-6229-4e13-b374-0a0a326c26aa_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>
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    <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>
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    <link:label id="lab_us-gaap_ValuationTechniqueAxis_1e489fa2-7010-4537-ad53-699faa0b9c20_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>
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    <link:label id="lab_kg_PremiumsEarnedNetAsPercentOfTotal_f92788e8-9ac0-484c-a74a-d686fd45537a_terseLabel_en-US" xlink:label="lab_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total Net premiums earned</link:label>
    <link:label id="lab_kg_PremiumsEarnedNetAsPercentOfTotal_label_en-US" xlink:label="lab_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Earned, Net as a Percent of Total</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumsEarnedNetAsPercentOfTotal" xlink:href="kg-20251231.xsd#kg_PremiumsEarnedNetAsPercentOfTotal"/>
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    <link:label id="lab_kg_NumberOfDirectors_1002f248-cd02-45f6-b6fa-bf60739e6aa3_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-20251231.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_kg_BarryZyskindMember_019b0161-beb7-7cd6-a764-6c09a78419e9_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-20251231.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_us-gaap_PropertyPlantAndEquipmentTypeDomain_dcce25d3-e265-4054-8390-7155b55120ba_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Long-Lived Tangible Asset [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentTypeDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentTypeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SeniorNotes2016Member_8d8491ee-7a88-4a5a-943f-06929b3f6798_verboseLabel_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2016 Senior Notes - MHLA &#8211; 6.625%</link:label>
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    <link:label id="lab_kg_SeniorNotes2016Member_label_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Senior Notes 2016 [Member]</link:label>
    <link:label id="lab_kg_SeniorNotes2016Member_documentation_en-US" xlink:label="lab_kg_SeniorNotes2016Member" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Senior Notes 2016 [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SeniorNotes2016Member" xlink:href="kg-20251231.xsd#kg_SeniorNotes2016Member"/>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock4Member_019caf7d-d46e-754f-bfd8-4123273ee576_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-20251231.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_us-gaap_DisposalGroupClassificationDomain_62d5562f-eb59-46f0-b6fc-fb9249b075b0_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_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance_cfb95130-b4e8-4288-862e-cd0f5a399e79_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Capital and Surplus</link:label>
    <link:label id="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance_42aa697f-947c-472b-a5cf-1efb43f514f0_verboseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Statutory capital and surplus</link:label>
    <link:label id="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance_label_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practices, Statutory Capital and Surplus, Balance</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance" xlink:to="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusBalance" 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_08783a64-7afa-4479-abc1-224f9723de4f_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 expense, debt issuance costs</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_us-gaap_InvestmentIncomeInvestmentExpense_97feceb7-6cdd-4a4a-bd39-c482eda37d50_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_ada061f4-b0db-4e57-8997-db78c8d63291_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_642c5c7a-fe35-4cf1-af95-fdd61f7376c4_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_7ccc9596-be5e-4d15-bae8-1f9e9c08f01f_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"/>
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    <link:label id="lab_kg_PostTerminationEndorsementNo.2Member_9eb8abe2-38c6-4e78-929f-ccc6cad5a3d3_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-20251231.xsd#kg_PostTerminationEndorsementNo.2Member"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTen_c40272ec-d413-479f-95d2-720ae2a508b9_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTen" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 10</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTen_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTen" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Historical Claims Duration, Year 10</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTen" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTen"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_749072ea-5d26-4b51-a8f9-8ff724c1bc5a_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Outstanding, ending balance (in dollars per share)</link:label>
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    <link:label id="lab_kg_LossContingencyPercentageOfOutstandingDebtHoldersInvolvedInLawsuit_83e97795-4a21-4540-8b89-2c1dd8bbf847_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-20251231.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_CommonStockSharesIssued_49c394aa-87aa-4887-90e8-bbd71be8cdd5_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_kg_EmployeeMember_3d6aecef-3229-49e2-a4b8-e95b3f927ce9_terseLabel_en-US" xlink:label="lab_kg_EmployeeMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Employee</link:label>
    <link:label id="lab_kg_EmployeeMember_label_en-US" xlink:label="lab_kg_EmployeeMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Employee [Member]</link:label>
    <link:label id="lab_kg_EmployeeMember_documentation_en-US" xlink:label="lab_kg_EmployeeMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Employee</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_EmployeeMember" xlink:href="kg-20251231.xsd#kg_EmployeeMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_EmployeeMember" xlink:to="lab_kg_EmployeeMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageRemainingLeaseTerm1_fffae095-1142-4664-a2ce-24749a008431_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_OtherPrivatelyHeldInvestmentsMember_f2e6a414-7e54-4275-991e-87d7238ce354_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>
    <link:label id="lab_kg_OtherPrivatelyHeldInvestmentsMember_label_en-US" xlink:label="lab_kg_OtherPrivatelyHeldInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other Privately Held Investments [Member]</link:label>
    <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-20251231.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_kg_ReconciliationtoNetIncomeLossAbstract_4b68c154-8d92-4f2c-9f9c-56e464da97fd_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 income</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-20251231.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_kg_PostTerminationEndorsementMinimumExcessFundingRequirementMember_9ff27499-0cfa-4b41-b34a-5ba593ffd40a_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-20251231.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_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember_bcef3954-9ef2-4dd4-a903-a96a390bf849_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:to="lab_us-gaap_MortgageBackedSecuritiesIssuedByUSGovernmentSponsoredEnterprisesMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityPublicFloat_3acc1b07-1213-4dba-b0e9-3a23fc1ff164_terseLabel_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:label id="lab_dei_EntityPublicFloat_label_en-US" xlink:label="lab_dei_EntityPublicFloat" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Public Float</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityPublicFloat" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityPublicFloat"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityPublicFloat" xlink:to="lab_dei_EntityPublicFloat" xlink:type="arc" order="1"/>
    <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_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_TotalShareholderRtnAmt" xlink:to="lab_ecd_TotalShareholderRtnAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_e36e5ccf-405c-4c48-a145-c619d5ed174a_terseLabel_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:label id="lab_us-gaap_LossContingenciesLineItems_label_en-US" xlink:label="lab_us-gaap_LossContingenciesLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Loss Contingencies [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LossContingenciesLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LossContingenciesLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LossContingenciesLineItems" xlink:to="lab_us-gaap_LossContingenciesLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_CorporateNonSegmentMember_47119b8d-5702-427e-ab9c-3bd0a59bc9f5_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_56b61d7c-abfd-48a6-a6d1-682c0bbebaec_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_IncomeTaxPaidForeignAfterRefundReceived_019cbc5c-0cfe-7a9d-9163-9359ef414da4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Foreign</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, Foreign, after Refund Received</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidForeignAfterRefundReceived"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:to="lab_us-gaap_IncomeTaxPaidForeignAfterRefundReceived" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ReinsuranceRecoverablesAllowance_6fc99238-90d3-4460-9ca3-18ecce74bac6_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_6c07dd31-6045-41f7-bd17-8b0be7b7159d_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_6a09b4e0-2a35-4d1c-920a-5a4a0b5f9df1_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_ReinsuranceCollateralByThirdParty_cd1dd69a-02f4-4dbc-ae4c-e0ed4cf0bc1a_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-20251231.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_kg_PostTerminationEndorsementNo.1Member_0011c896-7c15-4b46-9be7-7817d32f28c0_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-20251231.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_ShortDurationInsuranceContractAccidentYear2023Member_c9183601-7130-4d2a-9a1d-d9f4a401b179_terseLabel_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2023Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2023</link:label>
    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2023Member_label_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2023Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contract, Accident Year 2023 [Member]</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_47da12b4-4903-465e-848a-f1e5e43c7d65_terseLabel_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commission rate, percent of ceded written premiums</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_label_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Percent of Ceded Written Premiums</link:label>
    <link:label id="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Related Party Transaction, Commission Rate, Percent of Ceded Written Premiums</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums" xlink:href="kg-20251231.xsd#kg_RelatedPartyTransactionCommissionRatePercentOfCededWrittenPremiums"/>
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    <link:label id="lab_us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLossWriteoff_de8109d5-d143-41ec-8bba-2c5518379017_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, receivables</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_kg_LossContingencyAggregateCoverageAmount_019b02a5-3db2-7e72-9a5e-680ef687b409_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, coverage with aggregate limits</link:label>
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    <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>
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    <link:label id="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense_dcdc3d2b-0038-4aa6-a1cc-b662b1c17e56_verboseLabel_en-US" xlink:label="lab_us-gaap_SupplementalInformationForPropertyCasualtyInsuranceUnderwritersPriorYearClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net incurred losses related to Prior year</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_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsReplacedInPeriodWeightedAverageExercisePrice_019c3249-3222-77b4-9b12-7eb12a4ac4c3_terseLabel_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsReplacedInPeriodWeightedAverageExercisePrice" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Options replaced (in dollars per share)</link:label>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionAxis_889177f3-6097-4dd6-8140-d7fcb9f36148_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_kg_BusinessCombinationConsiderationTransferredIntercompanySettlement_7a9a12a0-5522-4178-b621-d8d9bc9f8881_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-20251231.xsd#kg_BusinessCombinationConsiderationTransferredIntercompanySettlement"/>
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    <link:label id="lab_kg_CollaborativeArrangementReservesExpectedToBeCommutedExitCost_6832e41f-1cb8-4244-a79a-3a9a5786fced_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>
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    <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-20251231.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_ValuationTechniqueDomain_354537b1-492b-461e-96bc-109eb0fc7a0b_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>
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    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetGainLossIncludedInOtherComprehensiveIncomeLoss_59f85d89-7e3e-468b-9382-c1f1fd25fe58_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 recognized in the statement of income</link:label>
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    <link:label id="lab_kg_OtherInvestmentsPercentOfTotal_11006ca4-78a4-4a81-aac1-2b0299efd81b_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>
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    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_d4f58710-eedd-45f7-8f59-a2e362496567_verboseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Interest in income of equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_f7240962-9379-4ec3-bf6d-a94d97a6dd9b_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 income of equity method investments</link:label>
    <link:label id="lab_us-gaap_IncomeLossFromEquityMethodInvestments_470bd10d-e930-4e05-b428-36cfa3f5874c_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 income from 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"/>
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    <link:label id="lab_kg_EuropeanHospitalInsuranceProductLineMember_6f6b40c9-3226-40c6-a979-1624d79384f5_terseLabel_en-US" xlink:label="lab_kg_EuropeanHospitalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">European Hospital Liability</link:label>
    <link:label id="lab_kg_EuropeanHospitalInsuranceProductLineMember_label_en-US" xlink:label="lab_kg_EuropeanHospitalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">European Hospital Insurance Product Line [Member]</link:label>
    <link:label id="lab_kg_EuropeanHospitalInsuranceProductLineMember_documentation_en-US" xlink:label="lab_kg_EuropeanHospitalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">European Hospital Insurance Product Line [Member]</link:label>
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    <link:label id="lab_us-gaap_UnearnedPremiums_6313f496-c151-4efa-a2d1-cacc4b594691_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 $17,227 from related parties in 2025)</link:label>
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    <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>
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    <link:label id="lab_us-gaap_AcquiredFiniteLivedIntangibleAssetsLineItems_d7297f92-09a7-4d9c-be02-736039d37307_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>
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    <link:label id="lab_country_SE_bceb4321-0904-408b-b283-afd5c8142f22_terseLabel_en-US" xlink:label="lab_country_SE" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Sweden</link:label>
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    <link:label id="lab_us-gaap_ShareBasedCompensationAbstract_74003a74-7e53-431b-8c1f-21755460b0fd_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Payment Arrangement, Noncash Expense [Abstract]</link:label>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsIncurredButNotReportedIbnrClaimsLiabilityNet_d76ef45c-e867-4d1e-8889-2080bef46428_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsIncurredButNotReportedIbnrClaimsLiabilityNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total IBNR</link:label>
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    <link:label id="lab_us-gaap_EarningsPerShareBasic_8d87b8f6-76af-408b-bbce-4218e70ec7c3_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 earnings (loss) per share available to Kestrel common shareholders (in dollars per share)</link:label>
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    <link:label id="lab_kg_ShortDurationInsuranceContractPolicyLimit_f270cdbb-5fc5-4d4b-afa3-96edaa002c84_terseLabel_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractPolicyLimit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Typical insurance limit</link:label>
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    <link:label id="lab_kg_ShortDurationInsuranceContractPolicyLimit_documentation_en-US" xlink:label="lab_kg_ShortDurationInsuranceContractPolicyLimit" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Short Duration Insurance Contract, Policy Limit</link:label>
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    <link:label id="lab_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossRollForward_260602de-cdc3-4e3c-b31c-4c4f7e6f1a5e_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>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsGross_7fa2f771-adb2-4977-b8c9-47ba207aa79a_totalLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsGross" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Deferred tax assets before valuation allowance</link:label>
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    <link:label id="lab_kg_DiversifiedReinsuranceSegmentMember_a23128ac-6e9c-4c42-a379-d6223df2a58d_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 Reinsurance</link:label>
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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>
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    <link:label id="lab_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember_019cdeee-b74c-7c90-98d6-f97209a60801_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>
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    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember" xlink:to="lab_us-gaap_MeasurementInputDiscountForLackOfMarketabilityMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness_2c808982-bd31-42e8-827d-c22695aadfe4_terseLabel_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net Maiden Legacy run-off business acquired</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness_label_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Assumed Business</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness_documentation_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Assumed Business</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness" xlink:href="kg-20251231.xsd#kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseAssumedBusiness"/>
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    <link:label id="lab_ecd_AwardTmgMnpiDiscTextBlock_terseLabel_en-US" xlink:label="lab_ecd_AwardTmgMnpiDiscTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Award Timing MNPI Disclosure</link:label>
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    <link:label id="lab_kg_AmTrustNorthAmericaIncMember_019b0161-beb7-7c51-a8de-8fcb8dc9a48c_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>
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    <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>
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    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_c3e65aff-5d93-4246-8105-8f320883595b_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>
    <link:label id="lab_us-gaap_OtherGeneralAndAdministrativeExpense_label_en-US" xlink:label="lab_us-gaap_OtherGeneralAndAdministrativeExpense" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Other General and Administrative Expense</link:label>
    <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_ScheduleOfInvestmentCreditRatingsTableTextBlock_9807c83a-a1ba-4259-bcf8-72278473f922_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>
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    <link:label id="lab_kg_OperatingLeaseEscalatingFeePercentage_0590c55c-8eae-445b-b11f-2fce2173cd04_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>
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    <link:label id="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover_2a442221-a2f8-4def-a026-306cf01a736e_terseLabel_en-US" xlink:label="lab_kg_ReinsuranceRecoverableForPaidAndUnpaidClaimsAndClaimsAdjustmentsAdverseDevelopmentCover" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adverse development cover</link:label>
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    <link:label id="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments_29740a9b-0b9b-4196-a6dc-accfcf6bfa3d_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireEquityMethodInvestments" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Purchases of equity method investments</link:label>
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    <link:label id="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent_194202c5-69d0-4727-8b3c-b6aa1cfdaced_terseLabel_en-US" xlink:label="lab_us-gaap_OciBeforeReclassificationsNetOfTaxAttributableToParent" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other comprehensive income before reclassifications</link:label>
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    <link:label id="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2020Member_37e9053a-b6cf-478e-a053-924c8c101747_terseLabel_en-US" xlink:label="lab_us-gaap_ShortDurationInsuranceContractAccidentYear2020Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2020</link:label>
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    <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"/>
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    <link:label id="lab_us-gaap_TreasuryStockCommonMember_f046898b-39ad-4683-8b3f-6da235246b9b_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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_0722a8be-357d-4145-94d8-399feb8e58de_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value of units vested</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" 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, Equity Instruments Other than Options, Vested in Period, Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodTotalFairValue"/>
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    <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"/>
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    <link:label id="lab_us-gaap_OperatingLeaseLiability_f8d594d3-717d-4551-b7d5-7342ed4133f6_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_0efaa272-34a9-4f5d-8080-5143c4856d6e_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_972e0bbd-e9c3-4d43-9abb-0a9c3a767c8c_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</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_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue_019c323b-76c0-707a-8815-cbce4d61e6cb_terseLabel_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards replaced (in dollars per share)</link:label>
    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue" 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, Equity Instruments Other Than Options, Replaced In Period, Weighted Average Grant Date Fair Value</link:label>
    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue_documentation_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-Based Compensation Arrangement By Share-Based Payment Award, Equity Instruments Other Than Options, Replaced In Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue" xlink:href="kg-20251231.xsd#kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsReplacedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncreaseDecreaseInUnearnedPremiums_5c22b1f1-4c7c-4beb-a024-bc28ff19e384_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_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_019b8fc5-eb86-738c-b759-fd62f95ab38a_terseLabel_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" 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_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" 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, Portion Attributable to Parent</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:to="lab_us-gaap_OtherComprehensiveIncomeForeignCurrencyTransactionAndTranslationAdjustmentNetOfTaxPortionAttributableToParent" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentBasisCurrencyEquivalentOfMaximumLimitOfLiabilityAttaching_f90cb678-c99e-437e-90ca-84708637837b_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-20251231.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_kg_PostTerminationEndorsementMaximumLossCorridorMember_a0407d47-a702-4e56-8968-7f239c2816ff_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-20251231.xsd#kg_PostTerminationEndorsementMaximumLossCorridorMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:to="lab_kg_PostTerminationEndorsementMaximumLossCorridorMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LiabilitiesAbstract_2f2ff31a-c26a-4f03-8e77-e830f3a9b760_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_4b6f3d7e-e786-44d6-98c1-a0667f3d3414_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_fe5c4693-67a4-4d5c-bb1d-e41d79adb7c3_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_RelatedPartyTransactionByTypeAxis_838efe5f-3506-40af-90ef-6c44c31391b7_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</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionByTypeAxis" xlink:href="kg-20251231.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_us-gaap_FairValueAssetsMeasuredOnRecurringBasisUnobservableInputReconciliationCalculationRollForward_6833539c-97fb-4276-ae27-4d863d9690a5_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"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationLineItems_5d4c80a9-3169-481d-9008-d8bedaea7da3_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration Insurance Contracts, Historical Claims Duration [Line Items]</link:label>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_190349ca-89da-44f6-aa60-1cdef15a942d_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">2028</link:label>
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    <link:label id="lab_kg_SeniorNotes2013Member_cf86e4e8-bd25-40d5-b7e8-67a47b637235_verboseLabel_en-US" xlink:label="lab_kg_SeniorNotes2013Member" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2013 Senior Notes - MHNC &#8211; 7.75%</link:label>
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    <link:label id="lab_us-gaap_DeferredFinanceCostsGross_f726629e-f746-49d0-ac30-44550c4caff3_verboseLabel_en-US" xlink:label="lab_us-gaap_DeferredFinanceCostsGross" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Original fair value adjustment at acquisition date</link:label>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesWithinOneYearFairValue_55d6e2f7-ded8-42b3-84ce-9b4032453496_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>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedReinsuranceRecoverableOnUnpaidLosses_db2aa176-b8d9-4ecd-bac2-9c76051431af_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>
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    <link:label id="lab_kg_SilverstoneVenture1Member_9bcaa779-7100-4c34-8715-33fadaf0597a_terseLabel_en-US" xlink:label="lab_kg_SilverstoneVenture1Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Silverstone Venture 1</link:label>
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    <link:label id="lab_us-gaap_ClassOfStockLineItems_3515dfa4-16c4-4182-86a6-d7d3c2d37a32_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>
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    <link:label id="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock_522d652a-815c-4c47-a01f-c9637716bf59_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>
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    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:to="lab_us-gaap_UnrealizedGainLossOnInvestmentsTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CollaborativeArrangementPaymentOfCommutedReserves_1658a681-9b81-44f9-8a4f-72c597e16b6e_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-20251231.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_WorkersCompensationInsuranceProductLineMember_c359fa07-4b37-42ff-9f09-bcfb435862a1_terseLabel_en-US" xlink:label="lab_kg_WorkersCompensationInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Workers' Compensation</link:label>
    <link:label id="lab_kg_WorkersCompensationInsuranceProductLineMember_label_en-US" xlink:label="lab_kg_WorkersCompensationInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Workers Compensation Insurance Product Line [Member]</link:label>
    <link:label id="lab_kg_WorkersCompensationInsuranceProductLineMember_documentation_en-US" xlink:label="lab_kg_WorkersCompensationInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Workers Compensation Insurance Product Line [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_WorkersCompensationInsuranceProductLineMember" xlink:href="kg-20251231.xsd#kg_WorkersCompensationInsuranceProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_WorkersCompensationInsuranceProductLineMember" xlink:to="lab_kg_WorkersCompensationInsuranceProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AELMember_faa7b5fa-a526-4d8d-9695-585af0a78bd5_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-20251231.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_kg_RelatedPartyTransactionPercentOfCededUnderwritingRiskInExchangeForCedingFee_019b0161-beb8-7a20-be1a-cf32fb93c39e_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-20251231.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_us-gaap_LongTermDebt_4c814629-8548-4d1d-be7b-73402b2ba1d8_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_b54f4a7f-d2bc-4208-9e97-99ef6b30458c_netLabel_en-US" xlink:label="lab_us-gaap_LongTermDebt" xlink:role="http://www.xbrl.org/2009/role/netLabel" 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_03ec9761-4da8-4ef5-960c-ab96c24b0d94_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_LegalEntityAxis" xlink:to="lab_dei_LegalEntityAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_Assets_837422db-8b59-48af-a7c0-293ec81a1924_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_56a91b19-bc09-4fa9-b0e3-697d5c84990d_terseLabel_en-US" xlink:label="lab_us-gaap_Assets" xlink:role="http://www.xbrl.org/2003/role/terseLabel" 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_kg_PremiumsWrittenNetAsPercentOfTotal_22432ab2-fa7a-4ce8-87b1-c475474c9034_terseLabel_en-US" xlink:label="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total Net premiums written</link:label>
    <link:label id="lab_kg_PremiumsWrittenNetAsPercentOfTotal_label_en-US" xlink:label="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Premiums Written, Net as a Percent of Total</link:label>
    <link:label id="lab_kg_PremiumsWrittenNetAsPercentOfTotal_documentation_en-US" xlink:label="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Premiums Written, Net as a Percent of Total</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:href="kg-20251231.xsd#kg_PremiumsWrittenNetAsPercentOfTotal"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:to="lab_kg_PremiumsWrittenNetAsPercentOfTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_019cd080-6783-7bdc-91b6-73688dda9766_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" 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_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths_label_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseNextTwelveMonths" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Finite-Lived Intangible Asset, Expected Amortization, Year One</link:label>
    <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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_c11ced86-f0eb-4241-bbb2-758e21431bb5_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Awards vested (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" 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, Equity Instruments Other than Options, Vested in Period, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriodWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue_d8546d5c-2c7d-4770-a7d4-1e50887484a8_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, 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-20251231.xsd#kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:to="lab_kg_AssetsFairValueDisclosureNumberOfSecuritiesPricedForFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_SegmentGeographicalDomain_dc71c2bb-717a-489f-a79f-1606496465fc_terseLabel_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Segment, Geographical [Domain]</link:label>
    <link:label id="lab_srt_SegmentGeographicalDomain_label_en-US" xlink:label="lab_srt_SegmentGeographicalDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_SegmentGeographicalDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_SegmentGeographicalDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_SegmentGeographicalDomain" xlink:to="lab_srt_SegmentGeographicalDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments_e8fc9405-9b54-44f8-99ce-138486d36d98_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-20251231.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments" xlink:to="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_1fe6b18c-fcee-4d2b-a696-0b352fce85d9_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Taxes</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxPolicyTextBlock" xlink:to="lab_us-gaap_IncomeTaxPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock_37fb308c-a180-490c-81bf-a669484a6daa_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Average Annual Payout of Net Loss and LAE</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Schedule of Historical Claims Duration [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsScheduleOfHistoricalClaimsDurationTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_1a8fe5c0-6664-4c30-ab2c-e330a5c5725d_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"/>
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    <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"/>
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    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges_019cbfa8-9733-7735-a99e-219d1165a502_terseLabel_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Adverse PPD reinsurance</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges_label_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges" 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, Net of Commission Changes</link:label>
    <link:label id="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges_documentation_en-US" xlink:label="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges" 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, Net of Commission Changes</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges" xlink:href="kg-20251231.xsd#kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges" xlink:to="lab_kg_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpensePeriodIncreaseNetOfCommissionChanges" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ConcentrationRiskByTypeAxis_4e495c72-f7f1-47bf-a4f4-ff8f92f4d11f_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_kg_MiscellaneousMember_32733cdf-015d-4b2f-867d-24a72121240a_verboseLabel_en-US" xlink:label="lab_kg_MiscellaneousMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Other run-off lines</link:label>
    <link:label id="lab_kg_MiscellaneousMember_f7bbd5d1-afae-42a5-9285-61c97fbb4960_terseLabel_en-US" xlink:label="lab_kg_MiscellaneousMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other reconciling items excluded from loss development tables</link:label>
    <link:label id="lab_kg_MiscellaneousMember_label_en-US" xlink:label="lab_kg_MiscellaneousMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Miscellaneous [Member]</link:label>
    <link:label id="lab_kg_MiscellaneousMember_documentation_en-US" xlink:label="lab_kg_MiscellaneousMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Miscellaneous [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MiscellaneousMember" xlink:href="kg-20251231.xsd#kg_MiscellaneousMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_MiscellaneousMember" xlink:to="lab_kg_MiscellaneousMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PrivateEquityFundsMember_6ccd10a9-142d-4a24-9367-e4bacc926e27_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_019cdf23-375f-7c87-8d13-403e4426c566_netLabel_en-US" xlink:label="lab_us-gaap_PrivateEquityFundsMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Privately held equity investments</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_ShortdurationInsuranceContractsClaimsDevelopmentTable_b7bd0394-1c85-4b68-8f79-ce9aed8c04a6_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration Insurance Contracts, Claims Development [Table]</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Claims Development [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsClaimsDevelopmentTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour_019cd080-96fa-76df-9819-4c656fd25a77_verboseLabel_en-US" xlink:label="lab_us-gaap_FiniteLivedIntangibleAssetsAmortizationExpenseYearFour" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">2029</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_OtherInvestments_8bf1c1cc-4563-4a15-af0a-98ee021797cc_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_7a7a270d-8b78-451d-90de-f3bc072fdd17_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</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_6c4194fe-e28b-484d-80c7-e706af2bfb66_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_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet_31401b9f-c2ec-4d3b-86f8-ef92d009efc0_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration insurance contracts, liability for unpaid claims and allocated claim adjustment expense, net</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet_4e3b342c-2bd6-4436-b7ac-8603c31ab4fe_totalLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Total net reserves including impact of LPT/ADC Agreement</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Liability for Unpaid Claims and Allocated Claim Adjustment Expense, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsLiabilityForUnpaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_6c2e31d3-090e-49c4-a185-4f93c12232e9_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_14c4caa4-aeab-4786-8d4a-e42b0a892394_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_839cd42a-5eb3-470e-ac69-6043f0a46992_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">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_dei_DocumentFinStmtErrorCorrectionFlag_68910ff5-e8f8-4522-a1ef-ff7d1e859338_terseLabel_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:label id="lab_dei_DocumentFinStmtErrorCorrectionFlag_label_en-US" xlink:label="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Document Financial Statement Error Correction [Flag]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_DocumentFinStmtErrorCorrectionFlag"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_DocumentFinStmtErrorCorrectionFlag" xlink:to="lab_dei_DocumentFinStmtErrorCorrectionFlag" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RestrictedInvestmentNetOfLiabilities_019b0101-b6d6-7d5e-b064-a46160f57059_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-20251231.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_us-gaap_EquityMethodInvestments_c3e13dc7-5037-47f2-b412-4867fd1016b1_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>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:to="lab_ecd_InsiderTrdPoliciesProcNotAdoptedTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ComputerSoftwareMember_2f384b75-9f7c-4d48-854e-9fb3589c4c8e_terseLabel_en-US" xlink:label="lab_kg_ComputerSoftwareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computer software</link:label>
    <link:label id="lab_kg_ComputerSoftwareMember_label_en-US" xlink:label="lab_kg_ComputerSoftwareMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Computer Software [Member]</link:label>
    <link:label id="lab_kg_ComputerSoftwareMember_documentation_en-US" xlink:label="lab_kg_ComputerSoftwareMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Computer Software</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ComputerSoftwareMember" xlink:href="kg-20251231.xsd#kg_ComputerSoftwareMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ComputerSoftwareMember" xlink:to="lab_kg_ComputerSoftwareMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessAcquisitionAcquireeDomain_515e9b2a-8237-4f7d-bb53-1e684c9f1ded_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:to="lab_us-gaap_BusinessAcquisitionAcquireeDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale_24e01a34-95d3-49c0-b3ee-51c519452b99_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>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale" xlink:href="kg-20251231.xsd#kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedFixedMaturitiesAvailableForSale"/>
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    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_019b0118-7178-7b7b-a4aa-11c33410593e_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">Equity method investments with fair value option elected</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_8ba1eddb-98c3-4466-bfe5-7004322f6939_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">Total unfunded commitments on equity method investments</link:label>
    <link:label id="lab_us-gaap_EquityMethodInvestmentsMember_6637e72d-1c10-4da2-be99-8bc670879d59_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">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_DiscontinuedOperationsPolicyTextBlock_e52648b7-2470-4239-8f9c-284310e75251_terseLabel_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discontinued Operations</link:label>
    <link:label id="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Discontinued Operations, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DiscontinuedOperationsPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:to="lab_us-gaap_DiscontinuedOperationsPolicyTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_50c4b136-bf5b-4dc2-a8de-f9c7e25321e2_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Income (Loss) Before Income Taxes and Total Income Tax Expenses</link:label>
    <link:label id="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock_label_en-US" xlink:label="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Schedule of Components of Income Tax Expense (Benefit) [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:to="lab_us-gaap_ScheduleOfComponentsOfIncomeTaxExpenseBenefitTableTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_PlanNameAxis_4f2689ad-e9a2-4f77-8170-44f9fce7143a_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_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_8fe89cf7-1df7-406a-af41-d0c6ab1de0e8_terseLabel_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Depreciable Fixed Assets</link:label>
    <link:label id="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock_label_en-US" xlink:label="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Property, Plant and Equipment, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PropertyPlantAndEquipmentPolicyTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" xlink:to="lab_us-gaap_PropertyPlantAndEquipmentPolicyTextBlock" 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_InternationalInsuranceProductLineMember_019b01de-34e7-7b46-8020-e9d524ab6783_netLabel_en-US" xlink:label="lab_kg_InternationalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">IIS business</link:label>
    <link:label id="lab_kg_InternationalInsuranceProductLineMember_aafdf0c8-7de7-4549-a9f6-79240f5c3454_terseLabel_en-US" xlink:label="lab_kg_InternationalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">International</link:label>
    <link:label id="lab_kg_InternationalInsuranceProductLineMember_230f98f6-0904-4108-a134-812e2a37c81d_verboseLabel_en-US" xlink:label="lab_kg_InternationalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">IIS business</link:label>
    <link:label id="lab_kg_InternationalInsuranceProductLineMember_label_en-US" xlink:label="lab_kg_InternationalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">International Insurance Product Line [Member]</link:label>
    <link:label id="lab_kg_InternationalInsuranceProductLineMember_documentation_en-US" xlink:label="lab_kg_InternationalInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">International Insurance Product Line [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_InternationalInsuranceProductLineMember" xlink:href="kg-20251231.xsd#kg_InternationalInsuranceProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InternationalInsuranceProductLineMember" xlink:to="lab_kg_InternationalInsuranceProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_ddccf7cf-61cd-4bc7-830e-91a707d36e21_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Acquired Level 3 financial assets</link:label>
    <link:label id="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3_label_en-US" xlink:label="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" 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 Transfers Into Level 3</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:to="lab_us-gaap_FairValueMeasurementWithUnobservableInputsReconciliationRecurringBasisAssetTransfersIntoLevel3" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_ecd80447-029c-404f-a79f-94a8aa8039cc_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>
    <link:label id="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock_label_en-US" xlink:label="lab_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Investments Classified by Contractual Maturity Date [Table Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InvestmentsClassifiedByContractualMaturityDateTableTextBlock"/>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments_6130e5a6-7d61-49b1-851a-201f0cde415d_totalLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesMinorityInterestAndIncomeLossFromEquityMethodInvestments" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before income taxes and interest in income of equity method investments</link:label>
    <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_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems_019cbc5c-0cfe-73ac-8968-799c30b2e37c_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Line Items]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionLineItems"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearSix_fd10eba4-d57d-4088-810d-85f3c8f72297_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearSix" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 6</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionPercentageOfRequiredFundingOnObligations_a2b15635-5614-4556-9f00-3508de62ffaf_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>
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    <link:label id="lab_country_US_019cbc6b-b044-771e-8dab-b03f1b1db4bb_verboseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">United States</link:label>
    <link:label id="lab_country_US_25cf525f-dd3b-4d1c-abb0-4d9aff79a603_terseLabel_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">U.S. taxes at statutory rates - Federal</link:label>
    <link:label id="lab_country_US_label_en-US" xlink:label="lab_country_US" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">UNITED STATES</link:label>
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    <link:label id="lab_kg_ComputerHardwareMember_97424f09-b517-47be-9f67-60564d422173_terseLabel_en-US" xlink:label="lab_kg_ComputerHardwareMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Computer hardware</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxReconciliationChangeInDeferredTaxAssetsValuationAllowance"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2008Member_66c70dcd-a494-4663-b15c-9757d1cc3461_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2008Member" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">2008</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2008Member_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYear2008Member" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Accident Year 2008 [Member]</link:label>
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    <link:label id="lab_us-gaap_RetainedEarningsMember_02878244-0fed-49ec-bf48-cf02aabb65ea_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"/>
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    <link:label id="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense_f1c8e2e1-c3ab-471a-b3fb-5dc3af9f9808_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_1f0cb88a-ac8a-4602-93f6-f6a7c539086d_terseLabel_en-US" xlink:label="lab_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_PaymentsForLossesAndLossAdjustmentExpense" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_PaymentsForLossesAndLossAdjustmentExpense"/>
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    <link:label id="lab_us-gaap_IncomeTaxAuthorityAxis_f88b42b3-ed84-4313-824d-0a521f42642e_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 Jurisdiction [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_kg_StandardPoorsBbbPlusBbbBbbMinusRatingMember_99f26fea-b03f-48ab-a877-bb833c960083_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>
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    <link:label id="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_d5e76b74-4797-49ef-9474-a0fe7691339b_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, cash equivalents and restricted cash - beginning of year</link:label>
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    <link:label id="lab_us-gaap_IncomeStatementAbstract_6509a493-6df6-47d2-bb2b-faa87af6110b_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">Income Statement [Abstract]</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>
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    <link:label id="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract_4a57e582-4bcc-430d-9f74-a4f7154e3467_terseLabel_en-US" xlink:label="lab_us-gaap_PremiumsWrittenNetConsolidatedAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Premiums written</link:label>
    <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_4ade99c5-b3e7-47a2-8a14-f0dab2d883ce_negatedLabel_en-US" xlink:label="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Purchases of fixed maturities</link:label>
    <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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:to="lab_us-gaap_PaymentsToAcquireMarketableSecurities" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense_1a56a936-9048-4f18-b9fe-c9eca768672a_terseLabel_en-US" xlink:label="lab_kg_InvestmentsGrossUnrealizedGainLossNetOfDeferredIncomeTaxExpense" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net unrealized gains, net of deferred income tax</link:label>
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    <link:label id="lab_kg_MarketableSecuritiesRealizedLoss_e539ce90-63df-47a3-bea6-72150b4f0e6c_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 loss</link:label>
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    <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-20251231.xsd#kg_MarketableSecuritiesRealizedLoss"/>
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    <link:label id="lab_us-gaap_InvestmentsFairValueDisclosure_ab3e8f53-9186-4fd8-a1f5-fed1a5d3f5c0_terseLabel_en-US" xlink:label="lab_us-gaap_InvestmentsFairValueDisclosure" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total Level 3 Investments</link:label>
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    <link:label id="lab_kg_BusinessCombinationStockConversionRatio_1bb7ee28-fd73-4815-a236-ad08e05c685c_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>
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    <link:label id="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember_572572ca-c200-4ad8-91cf-8567840dedb6_terseLabel_en-US" xlink:label="lab_kg_AmTrustQuotaSharesReinsuranceAgreementPartialTerminationAmendmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">AmTrust Quota Shares Reinsurance Agreement, Partial Termination Amendment and Commutation</link:label>
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    <link:label id="lab_kg_BusinessCombinationAcquisitionOptionTerm_019b0161-beb8-7669-9fd0-66b7c4fb3620_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>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationAcquisitionOptionTerm" xlink:href="kg-20251231.xsd#kg_BusinessCombinationAcquisitionOptionTerm"/>
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    <link:label id="lab_kg_RelatedPartyTransactionLoanAgreementObligationThreshold_aaf8a2b0-6e01-4349-a77c-6a4da3564828_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, obligation threshold</link:label>
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    <link:label id="lab_srt_ProductsAndServicesDomain_b7f2ecd3-e531-4485-88c0-bd567e6310c0_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>
    <link:label id="lab_srt_ProductsAndServicesDomain_label_en-US" xlink:label="lab_srt_ProductsAndServicesDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Product and Service [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_ProductsAndServicesDomain" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_ProductsAndServicesDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ProductsAndServicesDomain" xlink:to="lab_srt_ProductsAndServicesDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsPerDilutedShare_423592b0-75b6-433c-975b-9eba2e435be2_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 earnings (loss) from continuing operations per share attributable to Kestrel common 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"/>
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    <link:label id="lab_us-gaap_ReinsuranceRetentionExcessRetentionAmountReinsuredPerPolicy_5952d598-eea7-4ffb-aba7-b959ac0cb707_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"/>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNiMeasurementInput_019cdedd-91e3-782d-b0f9-09f8fa4b2a5f_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_f196dcde-4f16-4ef3-bc6c-bf3f78b2b5ce_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_d9896206-2420-4026-94fc-4b7d75ae0ed6_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"/>
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    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_019cbc5c-0cfe-79cd-9089-9cf27b958b8d_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable_label_en-US" xlink:label="lab_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Paid, by Individual Jurisdiction [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxPaidByIndividualJurisdictionTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxPaidByIndividualJurisdictionTable"/>
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    <link:label id="lab_us-gaap_ScheduleOfRecognizedIdentifiedAssetsAcquiredAndLiabilitiesAssumedTableTextBlock_02a7512a-d4b6-4125-81da-775fc341bf4d_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"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive_e476856f-0126-40a3-b0a4-a58fe476d7fb_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 5</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Historical Claims Duration, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentOwnership25PercentMember_019b0161-beb8-72f4-8f2d-9bdabc46f8db_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 Percent</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-20251231.xsd#kg_InvestmentOwnership25PercentMember"/>
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    <link:label id="lab_dei_CityAreaCode_e3ac56cd-5e3a-4166-8071-6d30eb53b9ad_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"/>
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    <link:label id="lab_kg_EquityMethodInvestmentUnrealizedGainLoss_019b0101-b6d6-7824-8e80-502edfa95c2c_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>
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    <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-20251231.xsd#kg_EquityMethodInvestmentUnrealizedGainLoss"/>
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    <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>
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    <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_EquityMethodInvestmentsRecordedWithEquityMethod_49a68b0d-2443-4f32-8728-5f29dde61e5e_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>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_EquityMethodInvestmentsRecordedWithEquityMethod" xlink:href="kg-20251231.xsd#kg_EquityMethodInvestmentsRecordedWithEquityMethod"/>
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    <link:label id="lab_kg_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpirationPercentage_cf822255-8363-4b36-98be-10a3b52d71b1_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>
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    <link:label id="lab_us-gaap_ScheduleOfTradingSecuritiesAndOtherTradingAssetsTable_b2246fd6-000d-4e91-a003-2dc43f0428f0_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"/>
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    <link:label id="lab_kg_IncreaseDecreaseInCashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsHeldForSale_0608cd03-2aff-4aca-b587-405b00f8cb6b_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>
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    <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>
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    <link:label id="lab_kg_FixedSecuritiesinUnrealizedLossPositionsQualitativeDisclosureNumberofPositions_ce8820e3-b2bb-48b6-bd31-35b590781f30_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-20251231.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_kg_BusinessCombinationConsiderationTransferredAttributableToPreCombinationService_87331d04-82a2-4e37-a5da-c1aad98f16f9_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-20251231.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_kg_ThirdPartyAgreementsMember_ec2a05e4-6ad9-4aed-8be3-68a0def3ae3b_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-20251231.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_NetCashProvidedByUsedInInvestingActivitiesAbstract_022107a1-b663-4184-bc5a-17f5888af21b_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_4660b187-e5ec-4b3c-bb9f-f2cb12b6aba7_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_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_kg_NumberOfIndependentDirectors_593f1605-f666-485b-aa3a-a4f667149d70_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-20251231.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_OperatingLeaseLiabilityStatementOfFinancialPositionExtensibleList_99133fea-07da-4212-8ace-5cfa8f9b187f_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_cccf8d61-42b6-4d66-9e15-3639cb9f9797_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_f65a5b3e-ac49-4cc4-80ac-6d28c4be6464_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_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_0dda867f-3b86-4d3d-98aa-44738b2b5568_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>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty_documentation_en-US" xlink:label="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:role="http://www.xbrl.org/2003/role/documentation" 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>
    <link:loc xlink:type="locator" xlink:label="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:href="kg-20251231.xsd#kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:to="lab_kg_RelatedPartyTransactionPercentOfLossesWithRespectToCurrentLinesOfBusinessExcludingThoseAboveCoveredBusinessThresholdToRelatedParty" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_019ca060-92f0-7a0a-8f85-3ac17f415e47_terseLabel_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
    <link:label id="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems_label_en-US" xlink:label="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Effective Income Tax Rate Reconciliation [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EffectiveIncomeTaxRateReconciliationLineItems"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:to="lab_us-gaap_EffectiveIncomeTaxRateReconciliationLineItems" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiCurrentAndNoncurrent_624f21a3-341a-40db-a312-3fbd3cfd5e19_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_0c652ed1-6636-4538-86cb-449a5d024242_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_7da54d98-5fc2-476a-a577-34433de79211_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"/>
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    <link:label id="lab_us-gaap_GainLossOnInvestments_8f9c2df2-7682-4fbe-97c1-642cc35beb18_verboseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestments" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" xlink:type="resource" xml:lang="en-US">Net realized and unrealized investment gains</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestments_b2947712-336d-481b-b2cc-7caa83e7f5c5_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_4fcf8bcb-7025-4320-8d17-5b8047ec4b31_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 (losses)</link:label>
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    <link:label id="lab_kg_StatutoryFinancialInformationAbstract_ef50255a-06f5-40bc-9043-85350b65ec28_terseLabel_en-US" xlink:label="lab_kg_StatutoryFinancialInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Financial Information [Abstract]</link:label>
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    <link:label id="lab_dei_AuditorName_1bffd690-e4e0-46e1-b7f6-39c2569005b7_terseLabel_en-US" xlink:label="lab_dei_AuditorName" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Name</link:label>
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    <link:label id="lab_us-gaap_ConcentrationRiskTable_7344a931-18bc-49d1-9934-61ad89a1f77c_terseLabel_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:label id="lab_us-gaap_ConcentrationRiskTable_label_en-US" xlink:label="lab_us-gaap_ConcentrationRiskTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Concentration Risk [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskTable" xlink:to="lab_us-gaap_ConcentrationRiskTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RelatedPartyTransactionPercentOfPremiumWrittenNetOfCostOfUnaffiliatedInuringReinsuranceFromRelatedParty_e3a12348-9b3e-4b6e-acab-f81a15ce8171_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-20251231.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_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDate_762366da-8e3e-44e6-abc0-c9fe0bfc246c_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"/>
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    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_deb1bb6e-0e46-40b5-96b9-f82821a41024_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</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_019b01ca-95af-7d24-98dd-1b22475b8534_netLabel_en-US" xlink:label="lab_kg_AmTrustReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Net favorable PPD for AmTrust Reinsurance legacy business</link:label>
    <link:label id="lab_kg_AmTrustReinsuranceSegmentMember_eeb7670b-acb2-4106-b3ad-a7d13cfbf9fa_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_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-20251231.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_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue_6d4790f9-45f8-40b3-ada8-551b636f0e23_terseLabel_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted average grant date fair value (in dollars per share)</link:label>
    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" 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, Options, Outstanding, Weighted Average Grant Date Fair Value</link:label>
    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue_documentation_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award, Options, Outstanding, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" xlink:href="kg-20251231.xsd#kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" xlink:to="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_19fd8b9d-35e3-40fc-b1de-d9ccaadfc207_terseLabel_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Supplemental cash flow information:</link:label>
    <link:label id="lab_us-gaap_SupplementalCashFlowInformationAbstract_label_en-US" xlink:label="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Supplemental Cash Flow Information [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SupplementalCashFlowInformationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SupplementalCashFlowInformationAbstract" xlink:to="lab_us-gaap_SupplementalCashFlowInformationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedCurrentAssetsReceivables_1dd78a5a-7af0-43ce-9478-e03bfe59bf1a_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>
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    <link:label id="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_dffae39a-71a9-46bf-90cc-d4ebaa1188a0_verboseLabel_en-US" xlink:label="lab_us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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_44bb1ebe-37d3-47b2-a139-13d24b76cb5c_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"/>
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    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_6425e1d6-f9e4-46d6-9b0d-d23b7e8bb0c4_negatedLabel_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other losses</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_cbed07c0-0f37-458b-8b3d-a694e47bca2b_negatedTerseLabel_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other losses</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_ab929346-4c2c-49b0-a827-968e9acba3c5_terseLabel_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign exchange and other losses, net</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_label_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Currency Transaction and Other Gain (Loss), before Tax</link:label>
    <link:label id="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax_documentation_en-US" xlink:label="lab_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Foreign Currency Transaction and Other Gain (Loss), before Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax" xlink:href="kg-20251231.xsd#kg_ForeignCurrencyTransactionandOtherGainLossbeforeTax"/>
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    <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"/>
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    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_0215b93a-c8ce-4e9b-a2d3-24045d205d92_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Weighted Average Exercise Price</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePriceRollforward" 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, Options, Outstanding, Weighted Average Exercise Price [Abstract]</link:label>
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    <link:label id="lab_kg_PrivatelyHeldEquityInvestmentsInPreferredStock1And2Member_019ce054-32c6-75a3-8d32-af5c47037d40_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>
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    <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>
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    <link:label id="lab_us-gaap_Dividends_861e0c25-b04e-424f-913f-cb1ff414f596_terseLabel_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:label id="lab_us-gaap_Dividends_label_en-US" xlink:label="lab_us-gaap_Dividends" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Dividends</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_Dividends" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_Dividends"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_Dividends" xlink:to="lab_us-gaap_Dividends" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_RelatedPartyDomain_855fd7b8-c087-45a3-8555-73bc1d2bbfed_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_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_019ce40a-d18b-7e2d-a4ad-7cb57aba336b_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Amount</link:label>
    <link:label id="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract_label_en-US" xlink:label="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Income Tax Expense (Benefit), Effective Income Tax Rate Reconciliation, Amount [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:to="lab_us-gaap_IncomeTaxExpenseBenefitContinuingOperationsIncomeTaxReconciliationAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable_34513d54-17fe-4dab-b742-64282914202b_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration Insurance Contracts, Reconciliation of Claims Development to Liability [Table]</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Reconciliation of Claims Development to Liability [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsReconciliationOfClaimsDevelopmentToLiabilityTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_NonPerformanceBasedRestrictedSharesMember_531ff491-e67e-494e-afc0-bdef75ae66ba_terseLabel_en-US" xlink:label="lab_kg_NonPerformanceBasedRestrictedSharesMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Non-Performance-Based Restricted Shares</link:label>
    <link:label id="lab_kg_NonPerformanceBasedRestrictedSharesMember_label_en-US" xlink:label="lab_kg_NonPerformanceBasedRestrictedSharesMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Non-Performance-Based Restricted Shares [Member]</link:label>
    <link:label id="lab_kg_NonPerformanceBasedRestrictedSharesMember_documentation_en-US" xlink:label="lab_kg_NonPerformanceBasedRestrictedSharesMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Non-Performance-Based Restricted Shares [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_NonPerformanceBasedRestrictedSharesMember" xlink:href="kg-20251231.xsd#kg_NonPerformanceBasedRestrictedSharesMember"/>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNiGainLoss_dd279dd6-709d-4441-9ad4-981ce8631110_totalLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:role="http://www.xbrl.org/2003/role/totalLabel" xlink:type="resource" xml:lang="en-US">Equity securities, net</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiGainLoss_aafb6a1d-397a-417c-b661-b02a57e8bd0b_terseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net gains recognized for equity securities</link:label>
    <link:label id="lab_us-gaap_EquitySecuritiesFvNiGainLoss_label_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Equity Securities, FV-NI, Gain (Loss)</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EquitySecuritiesFvNiGainLoss"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:to="lab_us-gaap_EquitySecuritiesFvNiGainLoss" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_VestingAxis_0301573d-7d79-4003-9428-ff823b146bca_terseLabel_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:label id="lab_us-gaap_VestingAxis_label_en-US" xlink:label="lab_us-gaap_VestingAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Vesting [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_VestingAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_VestingAxis"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_VestingAxis" xlink:to="lab_us-gaap_VestingAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueOfFinancialInstrumentsPolicy_b47ce872-849a-454b-9b37-07bab3b5c7e3_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_us-gaap_InvestmentsAbstract_020ca9e9-74e4-4ef7-b200-a2b61b6bc598_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_701cc5e6-fe6c-430b-a322-20c9124893de_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_kg_MaidenGFMember_a69361f3-3c19-419e-a6b8-1c9e9721e67c_terseLabel_en-US" xlink:label="lab_kg_MaidenGFMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Maiden GF</link:label>
    <link:label id="lab_kg_MaidenGFMember_label_en-US" xlink:label="lab_kg_MaidenGFMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Maiden GF [Member]</link:label>
    <link:label id="lab_kg_MaidenGFMember_documentation_en-US" xlink:label="lab_kg_MaidenGFMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Maiden GF [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_MaidenGFMember" xlink:href="kg-20251231.xsd#kg_MaidenGFMember"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInInvestingActivities_29d0307a-5650-4aea-b632-9220b7d1c945_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"/>
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    <link:label id="lab_kg_SilverstoneVenture2Member_ba7ebfcb-3ffd-4df7-9dff-6290ab3871a9_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-20251231.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_us-gaap_InterestPaidNet_ea03b474-eca4-4b7e-8b3c-68c7076c6d97_terseLabel_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash paid for interest, net of amounts capitalized</link:label>
    <link:label id="lab_us-gaap_InterestPaidNet_label_en-US" xlink:label="lab_us-gaap_InterestPaidNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Interest Paid, Excluding Capitalized Interest, Operating Activity</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_InterestPaidNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_InterestPaidNet"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_InterestPaidNet" xlink:to="lab_us-gaap_InterestPaidNet" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_DocumentFiscalYearFocus_6df94d9b-4791-478c-b07f-6a1540dda119_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_38fee0ef-b895-4a08-b4f4-7d671fd0609f_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_2f7638ca-040a-4f02-bf97-6aa3e251edd2_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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeituresWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_FairValueDisclosuresTextBlock_dfb2eac4-abf3-4410-a78c-f995266b8f78_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 Measurements</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_740c8170-c9b5-468d-b187-16d55830f8c1_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_us-gaap_CreditFacilityDomain_1b7030e9-c10d-41e9-bb77-1e738b78ef22_terseLabel_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:label id="lab_us-gaap_CreditFacilityDomain_label_en-US" xlink:label="lab_us-gaap_CreditFacilityDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Credit Facility [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CreditFacilityDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CreditFacilityDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CreditFacilityDomain" xlink:to="lab_us-gaap_CreditFacilityDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_d5ec967d-a332-4079-98f3-9dbb84524847_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Vesting percentage</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" 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, Award Vesting Rights, Percentage</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:to="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardAwardVestingRightsPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FurnitureAndEquipmentMember_019b58f5-55cd-7530-97e1-5e3ef17039e4_terseLabel_en-US" xlink:label="lab_kg_FurnitureAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Furniture and equipment</link:label>
    <link:label id="lab_kg_FurnitureAndEquipmentMember_label_en-US" xlink:label="lab_kg_FurnitureAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Furniture and Equipment [Member]</link:label>
    <link:label id="lab_kg_FurnitureAndEquipmentMember_documentation_en-US" xlink:label="lab_kg_FurnitureAndEquipmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Furniture and Equipment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_FurnitureAndEquipmentMember" xlink:href="kg-20251231.xsd#kg_FurnitureAndEquipmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FurnitureAndEquipmentMember" xlink:to="lab_kg_FurnitureAndEquipmentMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_GainLossOnEquityMethodInvestments_019b00fa-04ab-74fc-8e74-45d1261d9fa4_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-20251231.xsd#kg_GainLossOnEquityMethodInvestments"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_GainLossOnEquityMethodInvestments" xlink:to="lab_kg_GainLossOnEquityMethodInvestments" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage_95910512-6156-4acf-8134-8f34391e2e60_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_f63fc4d7-d3d9-4315-82f3-62f89797a5d7_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:to="lab_us-gaap_DebtInstrumentInterestRateStatedPercentage" xlink:type="arc" order="1"/>
    <link:label id="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis_c9287420-aee4-42c6-a598-1dcdee56f1f4_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:to="lab_srt_ScheduleOfEquityMethodInvestmentEquityMethodInvesteeNameAxis" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities_f0aea0ef-9847-4170-9afd-f198c2132e7a_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>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedEquitySecurities" xlink:href="kg-20251231.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_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock_d6a8319e-af5a-4226-bab0-1abb39d88b31_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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:to="lab_us-gaap_ScheduleOfEntityWideInformationRevenueFromExternalCustomersByProductsAndServicesTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_EntityVoluntaryFilers_7c75cbd1-163d-4e31-96e0-a97df6b741af_terseLabel_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:label id="lab_dei_EntityVoluntaryFilers_label_en-US" xlink:label="lab_dei_EntityVoluntaryFilers" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Entity Voluntary Filers</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_EntityVoluntaryFilers" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityVoluntaryFilers"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_EntityVoluntaryFilers" xlink:to="lab_dei_EntityVoluntaryFilers" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_MaidenHoldingsLtd.Member_67339c23-5a06-4a3c-a2e7-38bd936f3e8a_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-20251231.xsd#kg_MaidenHoldingsLtd.Member"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain_43291ab5-3405-4cb7-b837-6489bef920db_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration Insurance Contracts, Accident Year [Domain]</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Accident Year [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsAccidentYearDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SilverstoneVentureMember_019caf7a-8f79-7498-aab1-9855b1e65b71_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 Venture</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-20251231.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_DepreciationAmortizationAndAccretionNet_9cd11b04-89c1-4697-a776-2b9b5670ff5e_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, share-based compensation, 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_90d8ccf9-37e1-4576-b989-7c08a2f536e7_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>
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    <link:label id="lab_us-gaap_AssetsFairValueDisclosure_e9c5b1d1-e3c5-4983-be29-ee57bbc0d66f_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 Assets measured at Fair Value</link:label>
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    <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_us-gaap_ReinsuranceRecoverableAllowanceForCreditLossTableTextBlock_0f88567f-e3e0-4863-a83a-27bf4a458322_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>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_2cd207ba-6a57-446a-93f2-140ba9599b05_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>
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    <link:label id="lab_kg_SummaryOfOtherInvestmentsTableTextBlock_3425c816-0d2b-41d9-a039-f26f38303ff7_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>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInOperatingActivitiesContinuingOperations_4c865833-8be9-4e15-8103-928bb9714e00_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>
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    <link:label id="lab_us-gaap_TypeOfArrangementAxis_d4f3a393-5403-44a1-bab9-5eafbe92affd_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 Arrangements and Non-collaborative Arrangements [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>
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    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedNetLoanReceivableFromRelatedParty_24364890-ef5d-4343-8f3d-27abd236d9c6_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>
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    <link:label id="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit_3e21a021-9ce6-400a-b59a-b4c9c3dbf0d2_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredForeignIncomeTaxExpenseBenefit" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Deferred tax expense&#160;&#8211;&#160;Foreign (U.S. and others)</link:label>
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    <link:label id="lab_kg_KestrelGroupLLCMember_8b722937-6d5a-4a80-aaba-c43b82befad8_terseLabel_en-US" xlink:label="lab_kg_KestrelGroupLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Group LLC</link:label>
    <link:label id="lab_kg_KestrelGroupLLCMember_label_en-US" xlink:label="lab_kg_KestrelGroupLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Group LLC [Member]</link:label>
    <link:label id="lab_kg_KestrelGroupLLCMember_documentation_en-US" xlink:label="lab_kg_KestrelGroupLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Group LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelGroupLLCMember" xlink:href="kg-20251231.xsd#kg_KestrelGroupLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelGroupLLCMember" xlink:to="lab_kg_KestrelGroupLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InterestExpenseDebt_e673c8ba-9c74-4109-af92-3a0a94a9682c_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_kg_RealEstateInvestmentsAtEquityMethodMember_019b00c9-d49e-709e-a997-1e9e2b605a9d_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 valued at equity method of accounting</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-20251231.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_us-gaap_RestrictedInvestments_d9483f59-060e-4c72-bdf7-638dba0f51b8_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_2c903759-be60-4da2-a78b-835a7007fc71_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_8ade7e1e-b866-4a0f-bf75-9ae6fe66bbbd_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_EquityMethodInvestmentsInvesteeRevenue_42f06878-12c0-42ea-88cb-9698b5c3c8f7_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-20251231.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_us-gaap_DebtInstrumentFaceAmount_d33573fb-cd7c-448d-b50d-a60042687f24_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_kg_NumberOfInsuranceCarriers_8bf6578f-f6ab-451c-91a7-f9068f731f19_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-20251231.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_StatementOfIncomeAndComprehensiveIncomeAbstract_171e721e-8612-40b2-93f1-abf834fe3a53_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_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedLiabilitiesHeldForSale_0225a91f-20e9-46e1-8da5-87c23818e0b1_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-20251231.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_kg_InvestmentsFairValueOptionMember_019b00c3-1eec-7617-9a84-3fd1a0118a1e_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 (included in Other Investments)</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-20251231.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_BusinessCombinationConsiderationTransferredEquityInterestsIssuedAndIssuable_428b657f-d80e-4402-bda0-8861bfde1ebc_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_us-gaap_PreferredStockMember_923fcfc2-55fa-4b17-9f10-5aff0bc7622d_verboseLabel_en-US" xlink:label="lab_us-gaap_PreferredStockMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_5118eebf-8919-4010-8f2f-2f1555160c1d_periodEndLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Non-vested, ending balance (in dollars per share)</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" 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, Equity Instruments Other than Options, Nonvested, Weighted Average Grant Date Fair Value</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:to="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedWeightedAverageGrantDateFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo_39c7aef6-b3c2-4e6e-b939-280065b91cac_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 2</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Historical Claims Duration, Year Two</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearTwo" 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>
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    <link:label id="lab_us-gaap_OtherCommitment_f54b5351-ff69-49ec-bd64-8b02d832e7f8_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_dei_IcfrAuditorAttestationFlag_ffe74f53-8ad4-4101-846c-5b01d95f060b_terseLabel_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
    <link:label id="lab_dei_IcfrAuditorAttestationFlag_label_en-US" xlink:label="lab_dei_IcfrAuditorAttestationFlag" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">ICFR Auditor Attestation Flag</link:label>
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    <link:label id="lab_kg_PremiumRepaymentLoanAgreementMember_fdeebffa-ffc8-4145-80b5-3768ea261764_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>
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    <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-20251231.xsd#kg_PremiumRepaymentLoanAgreementMember"/>
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    <link:label id="lab_us-gaap_AlternativeInvestment_5ff79ec2-3fd8-4178-a8cc-55dca7e94435_verboseLabel_en-US" xlink:label="lab_us-gaap_AlternativeInvestment" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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"/>
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    <link:label id="lab_kg_RestrictedCashAndInvestmentsTypeDomain_019b0101-18a9-7fc4-837b-ece26bcfc97b_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-20251231.xsd#kg_RestrictedCashAndInvestmentsTypeDomain"/>
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    <link:label id="lab_us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_bd492593-d087-46b7-8409-a16cc8e48a6f_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>
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    <link:label id="lab_kg_KILHMember_019b0161-beb7-748c-b1f6-0ed2511d6e61_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-20251231.xsd#kg_KILHMember"/>
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    <link:label id="lab_srt_LitigationCaseAxis_019b02a5-3db2-7dc3-83fb-e26477976deb_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"/>
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    <link:label id="lab_us-gaap_ForeignCountryMember_019cbc5c-0cfe-7929-95cf-a722912f39ef_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Foreign Tax Jurisdiction [Member]</link:label>
    <link:label id="lab_us-gaap_ForeignCountryMember_label_en-US" xlink:label="lab_us-gaap_ForeignCountryMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Foreign Tax Jurisdiction [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ForeignCountryMember" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ForeignCountryMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ForeignCountryMember" xlink:to="lab_us-gaap_ForeignCountryMember" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_AuditorFirmId_35306077-febe-4d2c-95a2-f80c7cd1f488_terseLabel_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:label id="lab_dei_AuditorFirmId_label_en-US" xlink:label="lab_dei_AuditorFirmId" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Auditor Firm ID</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_AuditorFirmId" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AuditorFirmId"/>
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    <link:label id="lab_us-gaap_SegmentDomain_4a22391d-0b25-4daf-8ddc-55125845821f_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_2314e020-3bbd-4efd-8553-86eceb39e128_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_kg_PrivatelyHeldEquitySecuritiesInCommonStockMember_db986c0f-47bf-4429-832c-5acd186b04d4_terseLabel_en-US" xlink:label="lab_kg_PrivatelyHeldEquitySecuritiesInCommonStockMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Privately held common stocks</link:label>
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    <link:label id="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign_a48f3b07-3fbf-41e3-8202-a0370d773bfd_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeLossFromContinuingOperationsBeforeIncomeTaxesForeign" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Income (loss) before income taxes &#8211;&#160;Foreign (U.S. and others)</link:label>
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    <link:label id="lab_us-gaap_FixedMaturitiesMember_97f3b980-fd4a-4128-b6d2-aeb6b3cfd0cf_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_052362b2-2b4f-4524-8f58-c46dd6c58f38_terseLabel_en-US" xlink:label="lab_us-gaap_FixedMaturitiesMember" 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_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"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsCumulativePaidClaimsAndAllocatedClaimAdjustmentExpenseNet_890ff8b2-b5d8-4283-8a87-baae933125dc_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsCumulativePaidClaimsAndAllocatedClaimAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cumulative paid loss and LAE, net of reinsurance</link:label>
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    <link:label id="lab_kg_OCIDebtSecuritiesHeldForSaleUnrealizedHoldingGainLossBeforeAdjustmentAndTax_1362a727-8b5e-431e-99ef-58a9ed9b2353_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 gains on held for sale AFS investments</link:label>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearSeven_d2c2e9c9-8b12-4743-b84d-2f684e2ee975_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearSeven" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 7</link:label>
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    <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>
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    <link:label id="lab_us-gaap_PremiumsEarnedNet_fa8b567f-0ccd-4610-a3a3-6617816b29bc_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>
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    <link:label id="lab_kg_FixedMaturitiesFairValue_df76acde-63bc-484e-8dbb-b8b21f2e2001_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>
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    <link:label id="lab_srt_TitleOfIndividualAxis_label_en-US" xlink:label="lab_srt_TitleOfIndividualAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title and Position [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_TitleOfIndividualAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_TitleOfIndividualAxis"/>
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    <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"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInOperatingLiabilitiesAbstract_fdbeade3-9cc5-4e76-952e-8a130ade6d6c_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>
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    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_fd7afac2-5bcc-4929-9f9a-d3ac94607fc7_terseLabel_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cash acquired from purchase of business</link:label>
    <link:label id="lab_us-gaap_CashAcquiredFromAcquisition_label_en-US" xlink:label="lab_us-gaap_CashAcquiredFromAcquisition" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cash Acquired from Acquisition</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_CashAcquiredFromAcquisition" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_CashAcquiredFromAcquisition"/>
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    <link:label id="lab_us-gaap_FairValueMeasuredAtNetAssetValuePerShareMember_2dd3def7-5c06-4208-ab95-501ffb9c8f57_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"/>
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    <link:label id="lab_us-gaap_BusinessAcquisitionAxis_45d667c8-a0b2-4e66-9e00-c68cf8e2624a_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"/>
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    <link:label id="lab_kg_A2025EquityIncentivePlanMember_e368db31-5e7c-471f-a464-611c85be6d34_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-20251231.xsd#kg_A2025EquityIncentivePlanMember"/>
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    <link:label id="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_1b4efc19-0b71-4349-823f-6aafc1817b94_terseLabel_en-US" xlink:label="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Gross and Net Premiums Written and Net Premiums Earned by Geographic Location</link:label>
    <link:label id="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock_label_en-US" xlink:label="lab_us-gaap_RevenueFromExternalCustomersByGeographicAreasTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Revenue from External Customers by Geographic Areas [Table Text Block]</link:label>
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    <link:label id="lab_kg_QuotaShareReinsuranceAgreementsMember_6bdc02ac-e16b-4d6e-b5d2-cef1f183ecfb_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>
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    <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>
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    <link:label id="lab_us-gaap_InvestmentIncomeTextBlock_adf7d70e-f19c-4b1e-8e7b-3c4186c425b8_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>
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    <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_us-gaap_EquityMethodInvestmentOwnershipPercentage_a1c36c5d-c6fa-4d16-bfa7-18de97a9a861_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_bb209942-fbac-46d9-9b62-cc8f311f0bfd_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>
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    <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>
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    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryIndName" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryIndName"/>
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    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_15cd568d-2cab-4522-baac-dcdbf423cd99_terseLabel_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Expiration period (in years)</link:label>
    <link:label id="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod_label_en-US" xlink:label="lab_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" 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, Expiration Period</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardExpirationPeriod"/>
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    <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"/>
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    <link:label id="lab_us-gaap_BusinessCombinationContingentConsiderationAsset_019cbbb3-2bcb-7b2c-8452-20c58e0d851e_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_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_3888a6a9-04ac-4e3f-a807-5a51f5319ce1_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"/>
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    <link:label id="lab_us-gaap_DisposalGroupClassificationAxis_31b739ef-77ab-4a1c-a698-eb5796be0ba0_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_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract_41cc701d-3d56-407b-bb90-8bed3d10d036_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 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"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:to="lab_us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_InvestmentsContinuousUnrealizedLossPositionFairValue_b79e96ed-5e23-4979-b943-e6e66266fd55_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-20251231.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_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_d1f2da36-858c-4264-8524-c6d627e45ca8_terseLabel_en-US" xlink:label="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other Investments And Equity Method Investments</link:label>
    <link:label id="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember_2c4cafb4-42b0-4374-8bf3-d04960d710d0_verboseLabel_en-US" xlink:label="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:role="http://www.xbrl.org/2003/role/verboseLabel" 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-20251231.xsd#kg_OtherInvestmentsAndEquityMethodInvestmentsMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:to="lab_kg_OtherInvestmentsAndEquityMethodInvestmentsMember" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationOtherLiabilities_bc0e229e-ba9d-451b-95e7-88a7c182e5d6_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_kg_GrossPremiumsWrittenMember_fbd58e5e-d5ff-4a08-8471-bbe929af35df_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-20251231.xsd#kg_GrossPremiumsWrittenMember"/>
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    <link:label id="lab_srt_StatementGeographicalAxis_beddb14e-9e37-4edc-bcca-2ffa63105dc8_terseLabel_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:label id="lab_srt_StatementGeographicalAxis_label_en-US" xlink:label="lab_srt_StatementGeographicalAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Geographical [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_srt_StatementGeographicalAxis" xlink:href="https://xbrl.fasb.org/srt/2025/elts/srt-2025.xsd#srt_StatementGeographicalAxis"/>
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    <link:label id="lab_kg_InvestmentMilestoneTypeDomain_019b0161-beb8-7527-8fb1-646f244f6bbd_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-20251231.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_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>
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    <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_us-gaap_BusinessAcquisitionsProFormaRevenue_019ce34c-ff3f-7754-b8b4-c6b6c1476202_terseLabel_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total revenues</link:label>
    <link:label id="lab_us-gaap_BusinessAcquisitionsProFormaRevenue_label_en-US" xlink:label="lab_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Business Combination, Pro Forma Information, Pro Forma Revenue</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_BusinessAcquisitionsProFormaRevenue" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_BusinessAcquisitionsProFormaRevenue"/>
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    <link:label id="lab_us-gaap_StatutoryAccountingPracticesTable_751b4355-b55d-4614-bee1-cde93fd5564c_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practices [Table]</link:label>
    <link:label id="lab_us-gaap_StatutoryAccountingPracticesTable_label_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practices [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatutoryAccountingPracticesTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatutoryAccountingPracticesTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatutoryAccountingPracticesTable" xlink:to="lab_us-gaap_StatutoryAccountingPracticesTable" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_RealizedAndUnrealizedGainOnInvestments_c8734946-c256-4031-b1f7-f9d11345dd14_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>
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    <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_a3a00a17-5167-43bf-8dcd-90b4d2d84d99_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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ConcentrationRiskBenchmarkDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:to="lab_us-gaap_ConcentrationRiskBenchmarkDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_dei_Security12bTitle_5b98a408-07b4-4869-9228-9ac26dccd5e0_terseLabel_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:label id="lab_dei_Security12bTitle_label_en-US" xlink:label="lab_dei_Security12bTitle" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Title of 12(b) Security</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_dei_Security12bTitle" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_Security12bTitle"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_dei_Security12bTitle" xlink:to="lab_dei_Security12bTitle" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves_e61c10db-6ca1-4db9-813d-8197615ca0ff_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Discounting of net loss and LAE reserves</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Assets, Tax Deferred Expense, Reserves and Accruals, Loss Reserves</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves" xlink:to="lab_us-gaap_DeferredTaxAssetsTaxDeferredExpenseReservesAndAccrualsLossReserves" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_787db88d-8b7a-4f3b-9e59-1c7bd1230cf4_terseLabel_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:label id="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable_label_en-US" xlink:label="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Disposal Groups, Including Discontinued Operations [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:to="lab_us-gaap_IncomeStatementBalanceSheetAndAdditionalDisclosuresByDisposalGroupsIncludingDiscontinuedOperationsTable" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_da54cf83-cd33-4f7a-961d-9b5f034ba474_terseLabel_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:label id="lab_us-gaap_EarningsPerShareAbstract_label_en-US" xlink:label="lab_us-gaap_EarningsPerShareAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Earnings Per Share [Abstract]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_EarningsPerShareAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_EarningsPerShareAbstract"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_EarningsPerShareAbstract" xlink:to="lab_us-gaap_EarningsPerShareAbstract" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_StatutoryAccountingPracticesJurisdictionDomain_77686ce1-9617-4095-a510-468d9dc8ddeb_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesJurisdictionDomain" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practice, Jurisdiction [Domain]</link:label>
    <link:label id="lab_us-gaap_StatutoryAccountingPracticesJurisdictionDomain_label_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesJurisdictionDomain" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Statutory Accounting Practice, Jurisdiction [Domain]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StatutoryAccountingPracticesJurisdictionDomain" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StatutoryAccountingPracticesJurisdictionDomain"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StatutoryAccountingPracticesJurisdictionDomain" xlink:to="lab_us-gaap_StatutoryAccountingPracticesJurisdictionDomain" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_ff7a32b1-fd4a-4708-894a-78868fabd3c0_terseLabel_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" 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_LesseeOperatingLeaseLiabilityPaymentsDueYearFive_label_en-US" xlink:label="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Lessee, Operating Lease, Liability, to be Paid, Year Five</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:to="lab_us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearFive" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents_992ebe82-d879-496f-b780-a71fd8c9a8b1_terseLabel_en-US" xlink:label="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedRestrictedCashAndCashEquivalents" 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_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-20251231.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_kg_EuropeanHospitalLiabilityQuotaShareAgreementMember_d2564d5c-add6-416d-9bc0-dfe7b4078424_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-20251231.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_kg_KestrelIntermediateLedbetterHoldingsLLCMember_3424bd4e-09e1-4cbb-85c5-8dba76240d4c_terseLabel_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings, LLC</link:label>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsLLCMember_label_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings, LLC [Member]</link:label>
    <link:label id="lab_kg_KestrelIntermediateLedbetterHoldingsLLCMember_documentation_en-US" xlink:label="lab_kg_KestrelIntermediateLedbetterHoldingsLLCMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Kestrel Intermediate Ledbetter Holdings, LLC</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_KestrelIntermediateLedbetterHoldingsLLCMember" xlink:href="kg-20251231.xsd#kg_KestrelIntermediateLedbetterHoldingsLLCMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_KestrelIntermediateLedbetterHoldingsLLCMember" xlink:to="lab_kg_KestrelIntermediateLedbetterHoldingsLLCMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember_fa819451-8b17-4b94-9817-9b902ce71db7_terseLabel_en-US" xlink:label="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Commercial Auto Liability</link:label>
    <link:label id="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember_label_en-US" xlink:label="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Commercial Auto Liability Insurance Product Line [Member]</link:label>
    <link:label id="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember_documentation_en-US" xlink:label="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Commercial Auto Liability Insurance Product Line [Member]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CommercialAutoLiabilityInsuranceProductLineMember" xlink:href="kg-20251231.xsd#kg_CommercialAutoLiabilityInsuranceProductLineMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CommercialAutoLiabilityInsuranceProductLineMember" xlink:to="lab_kg_CommercialAutoLiabilityInsuranceProductLineMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_ReinsuranceAgreementOpen_b8ec6a32-01eb-41ae-b51f-9d016d2521bb_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>
    <link:label id="lab_kg_ReinsuranceAgreementOpen_label_en-US" xlink:label="lab_kg_ReinsuranceAgreementOpen" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance Agreement, Open</link:label>
    <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>
    <link:loc xlink:type="locator" xlink:label="loc_kg_ReinsuranceAgreementOpen" xlink:href="kg-20251231.xsd#kg_ReinsuranceAgreementOpen"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ReinsuranceAgreementOpen" xlink:to="lab_kg_ReinsuranceAgreementOpen" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine_fdd0affc-8d77-40d8-8b82-d2722e782049_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Year 9</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Historical Claims Duration, Year Nine</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine" xlink:to="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationYearNine" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue_3bbc9925-f73d-410a-9cda-87384998a9e9_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-20251231.xsd#kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:to="lab_kg_FixedMaturitiesContinuousUnrealizedLossPositionLessthanTwelveMonthsFairValue" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_CavelloMember_66242b26-a7db-463a-9baa-851d4b960b84_terseLabel_en-US" xlink:label="lab_kg_CavelloMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Cavello</link:label>
    <link:label id="lab_kg_CavelloMember_label_en-US" xlink:label="lab_kg_CavelloMember" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Cavello [Member]</link:label>
    <link:label id="lab_kg_CavelloMember_documentation_en-US" xlink:label="lab_kg_CavelloMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Cavello</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_CavelloMember" xlink:href="kg-20251231.xsd#kg_CavelloMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_CavelloMember" xlink:to="lab_kg_CavelloMember" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationContingentConsiderationAssetMeasurementInput_019cdee1-9b4c-7a81-a7b9-2a448fcbbbfa_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-20251231.xsd#kg_BusinessCombinationContingentConsiderationAssetMeasurementInput"/>
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    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationInvestmentIncomeNet_b0bf7844-a779-476f-94bc-51e1235aa00d_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>
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    <link:label id="lab_ecd_AwardTmgDiscLineItems_label_en-US" xlink:label="lab_ecd_AwardTmgDiscLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Award Timing Disclosures [Line Items]</link:label>
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    <link:label id="lab_us-gaap_OperatingLossCarryforwardsLineItems_label_en-US" xlink:label="lab_us-gaap_OperatingLossCarryforwardsLineItems" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Operating Loss Carryforwards [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OperatingLossCarryforwardsLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OperatingLossCarryforwardsLineItems"/>
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    <link:label id="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted_c4a879c8-6801-4aec-8a1f-f32b577733e7_negatedLabel_en-US" xlink:label="lab_us-gaap_UndistributedEarningsLossAllocatedToParticipatingSecuritiesDiluted" xlink:role="http://www.xbrl.org/2009/role/negatedLabel" xlink:type="resource" xml:lang="en-US">Amount allocated to participating common shareholders, diluted</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionByTypeDomain_375efef0-5ea5-4370-b2ff-1eb6b388bfa6_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>
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    <link:label id="lab_kg_FoundingShareholdersMember_aa845a9e-e5a1-44b5-8bc5-cf9260363f1c_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>
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    <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-20251231.xsd#kg_FoundingShareholdersMember"/>
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    <link:label id="lab_us-gaap_GainLossOnInvestmentsTextBlock_42d87b67-f1bf-4515-a5e1-b16cf1797ea6_terseLabel_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of Net Realized and Unrealized Investment Gains (Losses)</link:label>
    <link:label id="lab_us-gaap_GainLossOnInvestmentsTextBlock_label_en-US" xlink:label="lab_us-gaap_GainLossOnInvestmentsTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Gain (Loss) on Securities [Table Text Block]</link:label>
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    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet_1e04b9a0-007b-482d-bbdd-20dc53d2543b_periodStartLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE reserves, January 1</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet_0b9a2d01-dc92-4adc-bf84-4a5226b2d14d_periodEndLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel" xlink:type="resource" xml:lang="en-US">Net loss and LAE reserves, December 31</link:label>
    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet_label_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense, Net</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNet"/>
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    <link:label id="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_4fda8f5f-6399-410a-84e7-0e38e973698e_verboseLabel_en-US" xlink:label="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments" 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_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_982a6716-c19e-4f9e-9988-5171786266fe_terseLabel_en-US" xlink:label="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments" 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_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments_label_en-US" xlink:label="lab_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Fair Value, Investments, Entities that Calculate Net Asset Value Per Share, Unfunded Commitments</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommittments"/>
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    <link:label id="lab_kg_LesseeOperatingLeaseLiabilityFairValueDiscount_447e56da-466c-4da6-9336-a8f396322c2d_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-20251231.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_StockholdersEquityNoteDisclosureTextBlock_4d31c446-9664-4109-b979-be0251549c27_terseLabel_en-US" xlink:label="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Shareholders' Equity</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_StockholdersEquityNoteDisclosureTextBlock"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:to="lab_us-gaap_StockholdersEquityNoteDisclosureTextBlock" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_SummitReinsuranceSegmentMember_019c8f29-c98b-7158-b154-54a58d10e51b_terseLabel_en-US" xlink:label="lab_kg_SummitReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Summit Reinsurance Segment</link:label>
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    <link:label id="lab_kg_SummitReinsuranceSegmentMember_documentation_en-US" xlink:label="lab_kg_SummitReinsuranceSegmentMember" xlink:role="http://www.xbrl.org/2003/role/documentation" xlink:type="resource" xml:lang="en-US">Summit Reinsurance Segment</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_kg_SummitReinsuranceSegmentMember" xlink:href="kg-20251231.xsd#kg_SummitReinsuranceSegmentMember"/>
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    <link:label id="lab_us-gaap_ReinsuranceTextBlock_32471d60-4a86-4953-a935-8fbe794abf62_terseLabel_en-US" xlink:label="lab_us-gaap_ReinsuranceTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Reinsurance</link:label>
    <link:label id="lab_us-gaap_ReinsuranceTextBlock_label_en-US" xlink:label="lab_us-gaap_ReinsuranceTextBlock" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Reinsurance [Text Block]</link:label>
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    <link:label id="lab_us-gaap_NetIncomeLoss_58f6970c-ea1f-46b6-b772-d66184cfc280_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 income (loss)</link:label>
    <link:label id="lab_us-gaap_NetIncomeLoss_75ac738f-7646-45fd-9e34-ab07fddadc5a_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 income (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"/>
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    <link:label id="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems_f810444d-61f1-474d-95b2-702d1eff62f8_terseLabel_en-US" xlink:label="lab_us-gaap_SubsidiaryOrEquityMethodInvesteeLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Subsidiary or Equity Method Investee [Line Items]</link:label>
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    <link:label id="lab_kg_ProductsAndServicesSubtotalBeforeOtherItemsMember_dec5f45e-3bab-4107-a905-42b61c0fd8d2_terseLabel_en-US" xlink:label="lab_kg_ProductsAndServicesSubtotalBeforeOtherItemsMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Total</link:label>
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    <link:label id="lab_us-gaap_CollateralizedLoanObligationsMember_40b6c5e1-0e23-473d-a060-fd62bb60c592_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>
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    <link:label id="lab_kg_CashAndCashEquivalentsAndOtherMember_671c0cb0-4b00-49f1-bf76-7e85ef0f3fc7_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>
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    <link:label id="lab_us-gaap_SegmentReportingInformationLineItems_e286887e-26bc-45f0-8254-61757d9fcb94_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>
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    <link:label id="lab_us-gaap_LesseeOperatingLeaseTermOfContract_7608731f-4e69-43a6-9676-4ae89897dae8_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>
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    <link:label id="lab_us-gaap_MeasurementInputExpectedTermMember_019cdeec-6497-7a15-bbb7-b6c9a4f00b27_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>
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    <link:label id="lab_us-gaap_RetainedEarningsAccumulatedDeficit_838908c5-e74d-4aaf-bae6-e4e3e34d9474_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">Retained earnings (accumulated deficit)</link:label>
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    <link:label id="lab_kg_LPTADCAgreementMember_019b01cb-f52c-7244-97d0-eeb1aba4871f_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>
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    <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-20251231.xsd#kg_LPTADCAgreementMember"/>
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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>
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    <link:label id="lab_kg_EntitiesOwnedByRelatedPartiesAxis_6eecd5c4-09e5-44bf-b4a9-441ffd102dbb_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>
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    <link:label id="lab_us-gaap_DisposalGroupIncludingDiscontinuedOperationForeignCurrencyTranslationGainsLosses_3afc79f5-5246-47ee-9cf4-b8dbe8d8df41_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>
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    <link:label id="lab_kg_DeferredTaxLiabilitiesFairValueAdjustmentOnDebt_019c90a3-5623-7831-9b26-c4ecc01bf50c_terseLabel_en-US" xlink:label="lab_kg_DeferredTaxLiabilitiesFairValueAdjustmentOnDebt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Fair value adjustment for Senior Notes</link:label>
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    <link:label id="lab_us-gaap_FiniteLivedIntangibleAssetsNetAbstract_019cd0c5-2e75-78d5-9602-6a192b90b0ae_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 December&#160;31, 2025</link:label>
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    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_b1a6e107-cab0-4c67-a2d3-9e9477716313_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Others</link:label>
    <link:label id="lab_us-gaap_DeferredTaxLiabilitiesOther_label_en-US" xlink:label="lab_us-gaap_DeferredTaxLiabilitiesOther" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Deferred Tax Liabilities, Other</link:label>
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    <link:label id="lab_kg_DisposalGroupIncludingDiscontinuedOperationAccruedInvestmentIncome_ba554439-da15-4b71-a9fe-94f880e5973b_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>
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    <link:label id="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusRequired_026f6944-b83a-4758-b246-66f0fbfc2ef7_terseLabel_en-US" xlink:label="lab_us-gaap_StatutoryAccountingPracticesStatutoryCapitalAndSurplusRequired" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Minimum solvency margin</link:label>
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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>
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    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredIncomeTaxExpenseBenefit" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredIncomeTaxExpenseBenefit"/>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearAxis_6f45702f-0dcf-4fd1-8a72-1df97610ecb2_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearAxis" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration Insurance Contracts, Accident Year [Axis]</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearAxis_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsAccidentYearAxis" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Accident Year [Axis]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsAccidentYearAxis" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsAccidentYearAxis"/>
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    <link:label id="lab_us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_2a6c12aa-affd-471d-b22a-66e976ce679c_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>
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    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_a722e0a4-8cb7-466f-9b0f-52ecbb428452_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>
    <link:label id="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod_label_en-US" xlink:label="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Insurance Contracts, Program Fee Receivables, Premium Receivable, Collection Period</link:label>
    <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-20251231.xsd#kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:to="lab_kg_InsuranceContractsProgramFeeReceivablesPremiumReceivableCollectionPeriod" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ForeignTaxJurisdictionOtherMember_019ca062-6924-7ec7-95fc-10656189e9d9_terseLabel_en-US" xlink:label="lab_us-gaap_ForeignTaxJurisdictionOtherMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Other jurisdictions</link:label>
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    <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>
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    <link:label id="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock_019b58e4-6c5e-7650-8d87-a90cc4b57157_terseLabel_en-US" xlink:label="lab_us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsDisclosureTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Organization</link:label>
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    <link:label id="lab_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal_f00c2e03-70ae-4435-8752-83a93000541e_terseLabel_en-US" xlink:label="lab_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">% of Total</link:label>
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    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal" xlink:to="lab_kg_FairValueInvestmentsEntitiesThatCalculateNetAssetValuePerShareUnfundedCommitmentsPercentageOfTotal" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_InvestmentTypeExtensibleEnumeration_91e5538c-fcd3-4c75-8e70-63d5fcac80c6_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>
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    <link:label id="lab_kg_AmtrustQuotaShareReinsuranceSegmentMember_ccf01135-1e7d-4043-ac21-03e02dafcdf7_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>
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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>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesFairValueAbstract_344d3545-c3e1-4140-af12-5b7fbed165da_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>
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    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_4b1e2aec-ca3e-4916-b6a7-a79696d8b2be_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 $554,507 from related parties in 2025)</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_1dc2f61d-8abf-4a87-aa47-6226638d4607_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">Reverse for loss and loss adjustment expenses</link:label>
    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_3b5282a6-2dbb-4e6a-ac82-eaa28f77aea7_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>
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    <link:label id="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense_97905209-4f59-472d-9093-75a3167f8d87_netLabel_en-US" xlink:label="lab_us-gaap_LiabilityForClaimsAndClaimsAdjustmentExpense" xlink:role="http://www.xbrl.org/2009/role/netLabel" xlink:type="resource" xml:lang="en-US">Total Gross Reserves</link:label>
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    <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>
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    <link:label id="lab_us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_2f13fb7d-c4ee-449d-b5e7-f77fbae9b76f_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:label id="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_0c05edc3-17c5-4fcf-8766-941244b60457_terseLabel_en-US" xlink:label="lab_us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Schedule of All Share Option Activity</link:label>
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    <link:label id="lab_us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_449acdcc-a378-4e66-8edb-82f79d7af32f_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>
    <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_kg_NotesReceivableRelatedPartyMember_346e90d9-53fb-46ef-838e-33cd4588e1c1_terseLabel_en-US" xlink:label="lab_kg_NotesReceivableRelatedPartyMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Interest income from net loan receivable from AmTrust</link:label>
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    <link:label id="lab_us-gaap_ScheduleOfEarningsPerShareBasicAndDilutedTableTextBlock_40f78089-f50c-40d2-b036-2de5f5bed9cb_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_ScheduleOfInvestmentsReconciliationTableTextBlock_39130935-4ade-4ac4-b4c4-d91308cbac6c_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>
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    <link:label id="lab_srt_DirectorMember_111f704a-7794-4976-952c-20a5ddf44d9d_terseLabel_en-US" xlink:label="lab_srt_DirectorMember" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Director</link:label>
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    <link:label id="lab_kg_RelatedPartyTransactionFuturePremiumsandLossesRelatedtoPolicies_8cebdf59-6eb2-4aea-94e5-6a1353922cf9_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>
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    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationTable_c3b18bad-58d8-4fe2-b008-aa7b8081e6e1_terseLabel_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationTable" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Short-duration Insurance Contracts, Historical Claims Duration [Table]</link:label>
    <link:label id="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationTable_label_en-US" xlink:label="lab_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationTable" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Short-Duration Insurance Contracts, Historical Claims Duration [Table]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationTable" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShortdurationInsuranceContractsHistoricalClaimsDurationTable"/>
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    <link:label id="lab_us-gaap_RelatedPartyTransactionDomain_735e4dcc-e474-46cf-a1f0-f523f2070477_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"/>
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    <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_51c4fe0e-6cf4-4784-907f-90acfef35638_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>
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    <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"/>
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    <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>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DebtDisclosureAbstract" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DebtDisclosureAbstract"/>
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    <link:label id="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOrCashOptionValue_20404987-2b71-4a68-97d7-38324856f224_terseLabel_en-US" xlink:label="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOrCashOptionValue" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Compensation value issued to directors, in form of equity or cash</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOrCashOptionValue" xlink:href="kg-20251231.xsd#kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOrCashOptionValue"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOrCashOptionValue" xlink:to="lab_kg_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOrCashOptionValue" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy_086aa7fd-4e3c-4e87-87df-d338f573fec0_terseLabel_en-US" xlink:label="lab_us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy" 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_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy_label_en-US" xlink:label="lab_us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Unpaid Policy Claims and Claims Adjustment Expense, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy" xlink:to="lab_us-gaap_UnpaidPolicyClaimsAndClaimsAdjustmentExpensePolicy" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_BusinessCombinationRecognizedIdentifiableAssetsAcquiredAndLiabilitiesAssumedUnearnedPremiums_cf91dab2-29d8-47c1-8992-d2dd9dfb0b53_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-20251231.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_us-gaap_DebtSecuritiesAvailableForSaleRealizedGainLoss_04a37f0e-91b1-491f-b5c5-1e5b80dcbcca_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_bfef3fec-3330-4889-9cb6-229830b72b56_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 gains on fixed maturity investments arising during the year</link:label>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax_label_en-US" xlink:label="lab_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">OCI, Debt Securities, Available-for-Sale, Unrealized Holding Gain (Loss), before Adjustment and Tax</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodBeforeTax"/>
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    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_terseLabel_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:label id="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt_label_en-US" xlink:label="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Forgone Recovery due to Expense of Enforcement, Amount</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:href="https://xbrl.sec.gov/ecd/2025/ecd-2025.xsd#ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:to="lab_ecd_ForgoneRecoveryDueToExpenseOfEnforcementAmt" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_ebde94f5-b8e3-4f3c-ad12-f1470a9764d6_terseLabel_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Share-based Compensation Arrangement by Share-based Payment Award [Line Items]</link:label>
    <link:label id="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems_label_en-US" xlink:label="lab_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" 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 [Line Items]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems"/>
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    <link:label id="lab_srt_ConsolidatedEntitiesAxis_6b0604b5-fdb0-4a7c-92ae-b1205fb34813_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"/>
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    <link:label id="lab_us-gaap_CommonStockParOrStatedValuePerShare_7c3816aa-6fc4-4d50-8eb4-568053c4ec2d_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"/>
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    <link:label id="lab_kg_MeasurementInputDurationMatchedDiscountRatesMember_019cdee9-31b2-7d36-ad31-cfb0d05e675e_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>
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    <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-20251231.xsd#kg_MeasurementInputDurationMatchedDiscountRatesMember"/>
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    <link:label id="lab_kg_WeightedAverageAmortizationPeriodAbstract_019cd0cd-d9fe-7efa-968a-1a117738f05a_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>
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    <link:label id="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss_9db3a0be-1718-4ebb-8145-a5e106c20bf0_negatedTerseLabel_en-US" xlink:label="lab_us-gaap_EquitySecuritiesFvNiRealizedGainLoss" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel" xlink:type="resource" xml:lang="en-US">Net gains recognized for equity securities divested</link:label>
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    <link:label id="lab_kg_AmTrustQuotaShareMember_c10e6e0a-9fad-4acc-bf52-57b186d0179f_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>
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    <link:label id="lab_us-gaap_UseOfEstimates_4a3aa350-dc51-4547-be83-a398c6d2d9be_terseLabel_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Estimates</link:label>
    <link:label id="lab_us-gaap_UseOfEstimates_label_en-US" xlink:label="lab_us-gaap_UseOfEstimates" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Use of Estimates, Policy [Policy Text Block]</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_UseOfEstimates" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_UseOfEstimates"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_UseOfEstimates" xlink:to="lab_us-gaap_UseOfEstimates" xlink:type="arc" order="1"/>
    <link:label id="lab_us-gaap_OtherComprehensiveIncomeLossTaxPortionAttributableToParent1_7fb1e800-1f5b-42e0-b40d-534f647e2720_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 gain</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_OtherInvestmentMember_a14dfa43-31dd-4c3c-bf16-bd08029d88ac_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-20251231.xsd#kg_OtherInvestmentMember"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_kg_OtherInvestmentMember" xlink:to="lab_kg_OtherInvestmentMember" 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"/>
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    <link:label id="lab_us-gaap_IncreaseDecreaseInReinsuranceRecoverable_a89c03c5-e50f-4305-844a-c518952913e3_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>
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    <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"/>
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    <link:label id="lab_us-gaap_InvestmentIncomeInterestAndDividend_64880fdb-dfde-40d2-8417-4efef6c6aebc_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_eec4a60e-26f9-4ac1-bc0d-15e1b49ebd81_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>
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    <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"/>
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    <link:label id="lab_us-gaap_Liabilities_78c06f39-22a7-4835-a04f-f8bb0670097f_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_ControllingInterestOwnershipPercentage_c74ce44b-b404-4ccd-bcdc-04c4b7789fb4_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-20251231.xsd#kg_ControllingInterestOwnershipPercentage"/>
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    <link:label id="lab_us-gaap_AvailableForSaleSecuritiesDebtMaturitiesSingleMaturityDateAmortizedCostBasis_a1778aa8-ad99-4797-9b30-750a205d5fb4_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>
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    <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_3c4d0a1d-ca36-4afc-8c16-8895ee3b9577_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_1ced5dfd-ce30-4ba1-b900-0c2e854ee6a1_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>
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    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_d57dd99e-db67-4291-88e0-4ea20768268e_terseLabel_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net operating loss carryforwards, with no expiry date, amount</link:label>
    <link:label id="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration_label_en-US" xlink:label="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" 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</link:label>
    <link:loc xlink:type="locator" xlink:label="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:href="https://xbrl.fasb.org/us-gaap/2025/elts/us-gaap-2025.xsd#us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration"/>
    <link:labelArc xlink:arcrole="http://www.xbrl.org/2003/arcrole/concept-label" xlink:from="loc_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:to="lab_us-gaap_DeferredTaxAssetsOperatingLossCarryforwardsNotSubjectToExpiration" xlink:type="arc" order="1"/>
    <link:label id="lab_kg_AuditInformationAbstract_label_en-US" xlink:label="lab_kg_AuditInformationAbstract" xlink:role="http://www.xbrl.org/2003/role/label" xlink:type="resource" xml:lang="en-US">Audit Information [Abstract]</link:label>
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    <link:loc xlink:type="locator" xlink:label="loc_kg_AuditInformationAbstract" xlink:href="kg-20251231.xsd#kg_AuditInformationAbstract"/>
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    <link:label id="lab_kg_InsuranceLiabilitiesNet_3b663958-21d1-457a-9382-33398422757b_terseLabel_en-US" xlink:label="lab_kg_InsuranceLiabilitiesNet" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Net insurance liabilities</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-20251231.xsd#kg_InsuranceLiabilitiesNet"/>
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    <link:label id="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract_7867f422-90a0-4370-a3e7-e95305299e49_terseLabel_en-US" xlink:label="lab_us-gaap_LiabilityForUnpaidClaimsAndClaimsAdjustmentExpenseNetAbstract" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Liability for Unpaid Claims and Claims Adjustment Expense [Roll Forward]</link:label>
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    <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>
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    <link:label id="lab_dei_EntityIncorporationStateCountryCode_3e80e8f8-4b58-446e-af1d-07dfdf796b5b_terseLabel_en-US" xlink:label="lab_dei_EntityIncorporationStateCountryCode" xlink:role="http://www.xbrl.org/2003/role/terseLabel" xlink:type="resource" xml:lang="en-US">Entity Incorporation, State or Country Code</link:label>
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