In plain English
FAR 52.222-38, Compliance with Veterans’ Employment Reporting Requirements, is a solicitation provision prescribed at FAR 22.131, most recently dated Feb 2016. 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 22.1310(c), insert the following provision:
Prescribing reference: FAR 22.131.
The official text, verbatim
As prescribed in 22.1310(c), insert the following provision:
Compliance with Veterans’ Employment Reporting Requirements (Feb 2016)
By submission of its offer, the offeror represents that, if it is subject to the reporting requirements of 38 U.S.C. 4212(d)(i.e., if it has any contract containing Federal Acquisition Regulation clause 52.222-37, Employment Reports on Veterans), it has filed the most recent VETS-4212 Report required by that clause.
(End of provision)