In plain English
FAR 52.244-4, Subcontractors and Outside Associates and Consultants (Architect-Engineer Services), is a contract clause prescribed at FAR 44.204(b), most recently dated Aug 1998. 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 44.204(b), insert the following clause:
Prescribing reference: FAR 44.204(b).
The official text, verbatim
As prescribed in 44.204(b), insert the following clause:
Subcontractors and Outside Associates and Consultants (Architect-Engineer Services) (Aug 1998)
Any subcontractors and outside associates or consultants required by the Contractor in connection with the services covered by the contract will be limited to individuals or firms that were specifically identified and agreed to during negotiations. The Contractor shall obtain the Contracting Officer’s written consent before making any substitution for these subcontractors, associates, or consultants.
(End of clause)