In plain English
FAR 52.211-15, Defense Priority and Allocation Requirements, is a contract clause prescribed at FAR 11.604(b), most recently dated Apr 2008. 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 11.604(b), insert the following clause:
Prescribing reference: FAR 11.604(b).
The official text, verbatim
As prescribed in 11.604(b), insert the following clause:
Defense Priority and Allocation Requirement (Apr 2008)
This is a rated order certified for national defense, emergency preparedness, and energy program use, and the Contractor shall follow all the requirements of the Defense Priorities and Allocations System regulation (15 CFR 700).
(End of clause)