In plain English
FAR 52.217-6, Option for Increased Quantity, is a contract clause prescribed at FAR 17.208(d), most recently dated Mar 1989. 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 17.208(d), insert a clause substantially the same as the following:
Prescribing reference: FAR 17.208(d).
The official text, verbatim
As prescribed in 17.208(d), insert a clause substantially the same as the following:
Option for Increased Quantity (Mar 1989)
The Government may increase the quantity of supplies called for in the Schedule at the unit price specified. The Contracting Officer may exercise the option by written notice to the Contractor within ______________________ [insert in the clause the period of time in which the Contracting Officer has to exercise the option]. Delivery of the added items shall continue at the same rate as the like items called for under the contract, unless the parties otherwise agree.
(End of clause)