In plain English
FAR 52.208-7, Tagging of Leased Vehicles, is a contract clause prescribed at FAR 8.110, most recently dated May 1986. 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 8.1104(d), insert a clause substantially as follows:
Prescribing reference: FAR 8.110.
The official text, verbatim
As prescribed in 8.1104(d), insert a clause substantially as follows:
Tagging of Leased Vehicles (May 1986)
While it is the intent that vehicles leased under this contract will operate on Federal tags, the Government reserves the right to utilize State tags if necessary to accomplish its mission. Should State tags be required, the Contractor shall furnish the Government documentation necessary to allow acquisition of such tags. Federal tags are the responsibility of the Government.
(End of clause)