In plain English
FAR 52.236-25, Requirements for Registration of Designers, is a contract clause prescribed at FAR 36.609-4, most recently dated June 2003. 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 36.609-4 , insert the following clause:
Prescribing reference: FAR 36.609-4.
The official text, verbatim
As prescribed in 36.609-4 , insert the following clause:
Requirements for Registration of Designers (June 2003)
Architects or engineers registered to practice in the particular professional field involved in a State, the District of Columbia, or an outlying area of the United States shall prepare or review and approve the design of architectural, structural, mechanical, electrical, civil, or other engineering features of the work.
(End of clause)