How long does it take to receive continuation pay after you submitted for it?

Most pays take about a month. It's really a matter of when does the DFAS technician get around to processing your case, not how long does it take.

What is continuation pay?
A. BRS includes a Continuation Pay provision as a way to encourage Service members to continue serving in the Uniformed Services. Continuation Pay is a
direct cash payout, like a bonus. It is payable between the completion of eight years of service, but before completion of 12 years of service, as determined
and announced by your Service. Members receive Continuation Pay in return for additional obligated service. Active component service members
(including Active Guard Reserve (AGR) and Full Time Support (FTS)) enrolled in the BRS will be eligible for a cash incentive of 2.5 to 13 times their regular
monthly basic pay. Reserve Component members will be eligible for 0.5 to 6 times their monthly basic pay (as if serving on active duty). Each service will
publish guidance related to Continuation Pay rates. The rates for each calendar year will be determined by the retention needs of the Military Services and
published.