During IET, an "Advance Pay" of $350 is entitled, I was given 1. I was charged "Advance Pay" and "Repay Advance" both of $350. Is that wrong?

Basic double entry book keeping. It is correct. They didn't take it back twice, they showed it coming off the monthly pay, then you payed that back.

More details. Occurred three years ago. Reviewed all LES statements from entry into service to present.

Second month of service, received 1X "ADVANCE PAY" of $350 under entitlements, obviously the Eagle Cash Card I received.
Same month, 1X "ADVANCE PAY" of $350 is listed under deductions.
Same month, 1X "REPAY ADVANCE" of $350 is listed under deductions.
Under remarks, the line "REPAYMENT OF ADVANCE XXXXXX (XXX)" comes up twice in a row with the same code.
No other entitlements of $350 are found in any LES statements from entry to present.
No other related remarks come up in any other LES either.

Getting out soon, decided to review all LES's before I do to double-check for discrepancies.

If you only owed $350 and were charged double then someone goofed. Your S-1 should be able to straighten it out with Disbursing.