In plain English
FAR 52.219-13, Notice of Set-Aside of Orders, is a contract clause prescribed at FAR 19.507(f)(1), most recently dated Mar 2020. 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 19.507(f)(1), insert the following clause:
Prescribing reference: FAR 19.507(f)(1).
The official text, verbatim
As prescribed in 19.507(f)(1), insert the following clause:
Notice of Set-Aside of Orders (Mar 2020)
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(a) The Contracting Officer may set aside orders for the small business concerns identified in 19.000(a)(3).
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(b) The Contracting Officer will give notice of the order or orders, if any, to be set aside for small business concerns identified in 19.000(a)(3) and the applicable small business program. This notice, and its restrictions, will apply only to the specific orders that have been set aside for any of the small business concerns identified in 19.000(a)(3).
(End of clause)
Alternate I (Mar 2020) . As prescribed in 19.507(f)(2), substitute the following paragraph (a) for paragraph (a) of the basic clause:
(a) The Contracting Officer will set aside orders for the small business concerns identified in 19.000(a)(3) when the conditions of FAR 19.502-2 and the specific program eligibility requirements are met, as applicable.