In plain English
FAR 52.233-2, Service of Protest, is a solicitation provision prescribed at FAR 33.106, most recently dated Sept 2006. 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 33.106 , insert the following provision:
Prescribing reference: FAR 33.106.
The official text, verbatim
As prescribed in 33.106 , insert the following provision:
Service of Protest (Sept 2006)
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(a) Protests, as defined in section 33.101 of the Federal Acquisition Regulation, that are filed directly with an agency, and copies of any protests that are filed with the Government Accountability Office (GAO), shall be served on the Contracting Officer (addressed as follows) by obtaining written and dated acknowledgment of receipt from ______________________. [Contracting Officer designate the official or location where a protest may be served on the Contracting Officer.]
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(b) The copy of any protest shall be received in the office designated above within oneday of filing a protest with the GAO.
(End of provision)