In plain English
FAR 52.213-2, Invoices, is a contract clause prescribed at FAR 13.302-5(b), 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
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 13.302-5(b), insert the following clause:
Prescribing reference: FAR 13.302-5(b).
The official text, verbatim
As prescribed in 13.302-5(b), insert the following clause:
Invoices (Apr 1984)
The Contractor’s invoices must be submitted before payment can be made. The Contractor will be paid on the basis of the invoice, which must state-
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(a) The starting and ending dates of the subscription delivery; and
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(b) Either that orders have been placed in effect for the addressees required, or that the orders will be placed in effect upon receipt of payment.
(End of clause)