In plain English
FAR 52.214-22, Evaluation of Bids for Multiple Awards, is a solicitation provision prescribed at FAR 14.201-6(q), most recently dated Mar 1990. 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
This is a solicitation provision — it applies to offerors when submitting an offer, not to contract performance, so subcontract flowdown is generally not the operative question for it.
Where it's prescribed
As prescribed in 14.201-6(q), insert the following provision:
Prescribing reference: FAR 14.201-6(q).
The official text, verbatim
As prescribed in 14.201-6(q), insert the following provision:
Evaluation of Bids for Multiple Awards (Mar 1990)
In addition to other factors, bids will be evaluated on the basis of advantages and disadvantages to the Government that might result from making more than one award (multiple awards). It is assumed, for the purpose of evaluating bids, that $500 would be the administrative cost to the Government for issuing and administering each contract awarded under this solicitation, and individual awards will be for the items or combinations of items that result in the lowest aggregate cost to the Government, including the assumed administrative costs.
(End of provision)