<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001604665</issuerCik>
        <issuerName>Westlake Chemical Partners LP</issuerName>
        <issuerTradingSymbol>WLKP</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001299403</rptOwnerCik>
            <rptOwnerName>Chao Albert</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>2801 POST OAK BLVD</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 600</rptOwnerStreet2>
            <rptOwnerCity>HOUSTON</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>77056</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>1</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>President &amp; CEO</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Units (Limited Partner Interests)</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>3580</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>15.18</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>100015</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units (Limited Partner Interests)</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>27275</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>by Trusts</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Units (Limited Partner Interests)</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>14122230</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>TTWF LP &amp; TTWFGP LLC</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">The price reported in Column 4 is a weighted average price. These common units were purchased in multiple transactions ranging from $14.40 to $15.38, inclusive. The reporting person undertakes to provide to Westlake Chemical Partners LP, any security holder of Westlake Chemical Partners LP or the staff of the Securities and Exchange Commission, upon request, full information regarding the number of common units purchased at each separate price within the ranges set forth in this footnote.</footnote>
        <footnote id="F2">WPT LLC (&quot;WPT&quot;) owns 14,122,230 common units (&quot;Common Units&quot;) representing limited partner interests in the Issuer. Westlake Chemical Corporation (&quot;Westlake&quot;) owns 100% of each of Westlake Olefins LLC (&quot;Olefins&quot;), Westlake Vinyl Corporation (&quot;Vinyl&quot;) and Westlake Longview Corporation (&quot;Longview&quot;). Olefins owns 100% of Westlake Chemical Investments, lnc., which owns 84.25% of Westlake Polymers LLC (&quot;Polymers&quot;). Vinyl owns 100% of Westlake Vinyls, Inc., which owns 12.95% Polymers. Longview owns 2.80% of Polymers. Polymers owns 100% of WPT LLC. The reporting person may be deemed to indirectly own the Common Units through his ownership interest in TTWF LP, a Delaware limited partnership through which the reporting person indirectly holds 92,010,554 shares of Westlake.</footnote>
        <footnote id="F3">Two trusts for the benefit of members of the Chao family, including the reporting person, are the managers of TTWF GP LLC, a Delaware limited liability company that is the general partner of TTWF LP. The limited partners of TTWF LP are five trusts, principally for the benefit of members of the Chao family, including the reporting person, and two corporations owned, indirectly or directly, by certain of these trusts and by other entities owned by members of the Chao family, including the reporting person. The reporting person shares investment and voting power with respect to the common units beneficially owned by TTWF LP. The reporting person disclaims beneficial ownership of the Common Units except to the extent of his pecuniary interest therein.</footnote>
    </footnotes>

    <remarks>Mr. Albert Chao is a director and officer of Westlake Chemical Partners GP LLC, the general partner of Westlake Chemical Partners LP.</remarks>

    <ownerSignature>
        <signatureName>Albert Chao by J. Feng POA</signatureName>
        <signatureDate>2020-03-16</signatureDate>
    </ownerSignature>
</ownershipDocument>
