In plain English
FAR 52.222-10, Compliance with Copeland Act Requirements, is a contract clause prescribed at FAR 22.407(a), most recently dated Feb 1988. 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
We scanned the full clause text and found no sentence directing the contractor to insert this clause into subcontracts. That is a statement about the text, not legal advice: a prime contractor may still flow terms down contractually, an agency supplement (DFARS, VAAR, …) may add requirements, and clauses listed below (if any) may order this clause into subcontracts from the outside.
Where it's prescribed
As prescribed in 22.407(a), insert the following clause:
Prescribing reference: FAR 22.407(a).
The official text, verbatim
As prescribed in 22.407(a), insert the following clause:
Compliance with Copeland Act Requirements (Feb 1988)
The Contractor shall comply with the requirements of 29 CFR Part 3, which are hereby incorporated by reference in this contract.
(End of clause)