In plain English
FAR 52.216-1, Type of Contract, is a solicitation provision prescribed at FAR 16.105, most recently dated Apr 1984. 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 16.105 , complete and insert the following provision:
Prescribing reference: FAR 16.105.
The official text, verbatim
As prescribed in 16.105 , complete and insert the following provision:
Type of Contract (Apr 1984)
The Government contemplates award of a ______________ [Contracting Officer insert specific type of contract] contract resulting from this solicitation.
(End of provision)