In plain English
FAR 52.215-8, Order of Precedence-Uniform Contract Format, is a contract clause prescribed at FAR 15.209(h), most recently dated Oct 1997. 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 15.209(h), insert the following clause:
Prescribing reference: FAR 15.209(h).
The official text, verbatim
As prescribed in 15.209(h), insert the following clause:
Order of Precedence-uniform Contract Format (Oct 1997)
Any inconsistency in this solicitation or contract shall be resolved by giving precedence in the following order:
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(a) The Schedule (excluding the specifications).
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(b) Representations and other instructions.
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(c) Contract clauses.
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(d) Other documents, exhibits, and attachments.
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(e) The specifications.
(End of clause)