In plain English
FAR 52.232-15, Progress Payments Not Included, is a contract clause prescribed at FAR 32.502-3(c), most recently dated Apr 1984. 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 32.502-3(c), insert the following provision in invitations for bids if the solicitation will not contain one of the provisions prescribed in 32.502-3 (a) and (b):
Prescribing reference: FAR 32.502-3(c), FAR 32.502-3.
The official text, verbatim
As prescribed in 32.502-3(c), insert the following provision in invitations for bids if the solicitation will not contain one of the provisions prescribed in 32.502-3 (a) and (b):
Progress Payments Not Included (Apr 1984)
A progress payments clause is not included in this solicitation, and will not be added to the resulting contract at the time of award. Bids conditioned upon inclusion of a progress payment clause in the resulting contract will be rejected as nonresponsive.
(End of clause)