In plain English
FAR 52.232-13, Notice of Progress Payments, is a contract clause prescribed at FAR 32.502-3(a), 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(a), insert the following provision in invitations for bids and requests for proposals that include a Progress Payments clause:
Prescribing reference: FAR 32.502-3(a).
The official text, verbatim
As prescribed in 32.502-3(a), insert the following provision in invitations for bids and requests for proposals that include a Progress Payments clause:
Notice of Progress Payments (Apr 1984)
The need for customary progress payments conforming to the regulations in subpart 32.5 of the Federal Acquisition Regulation (FAR) will not be considered as a handicap or adverse factor in the award of the contract. The Progress Payments clause included in this solicitation will be included in any resulting contract, modified or altered if necessary in accordance with subsection 52.232-16 and its Alternate I of the FAR. Even though the clause is included in the contract, the clause shall be inoperative during any time the contractor’s accounting system and controls are determined by the Government to be inadequate for segregation and accumulation of contract costs.
(End of clause)