In plain English
FAR 52.204-1, Approval of Contract, is a contract clause prescribed at FAR 4.103, most recently dated Dec 1989. 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 4.103 , insert the following clause:
Prescribing reference: FAR 4.103.
The official text, verbatim
As prescribed in 4.103 , insert the following clause:
Approval of Contract (Dec 1989)
This contract is subject to the written approval of [identify title of designated agency official here] and shall not be binding until so approved.
(End of clause)