In plain English
FAR 52.219-31, Notice of Small Business Reserve, is a solicitation provision prescribed at FAR 19.507(g)(1), most recently dated Mar 2020. The complete official text is reproduced below, verbatim, from GSA's published FAR source files.
Its text contains no sentence requiring insertion into subcontracts; see the flowdown section below for what that does and does not mean.
Does it flow down to subcontracts?
No flowdown mandate found in the clause text
This is a solicitation provision — it applies to offerors when submitting an offer, not to contract performance, so subcontract flowdown is generally not the operative question for it.
Where it's prescribed
As prescribed in 19.507(g)(1), insert the following provision:
Prescribing reference: FAR 19.507(g)(1).
The official text, verbatim
As prescribed in 19.507(g)(1), insert the following provision:
Notice of Small Business Reserve (Mar 2020)
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(a) This solicitation contains a reserve for one or more small business concerns identified at 19.000(a)(3). The small business program eligibility requirements apply.
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(b) The small business concern(s) eligible for participation in the reserve shall submit one offer that addresses each portion of the solicitation for which it wants to compete. Award of the contract will be based on criteria identified elsewhere in the solicitation.
(End of provision)