Checkraising this flop is definitely the worst option when faced with 2 cold even calling stations can fold on an AKQ board.

I like bet\calling over check\calling.

TAG's raising range is fairly wide 11.3. This includes TT, 99, 88, KJ and whole bunch you could be ahead of here. He is passive post flop and a bet here is unlikely to, but could pick up the pot.

Due to villian's passive postflop stats, I think betting this flop will tell you how strong your hand is UI and is one of the very rare circumstances where the "information value" is worth it.

As you played it.

Once TAG 3bets your checkraise you know he has you beat at this point. His range does include AT, AJ definitely so your 2pr outs aren't completely gone but are pretty close. Your nut flush is ~neutral value and has slim edge, if any, at this point as you could be up against a set. Capping this flop depends on how likely it might buy you a free card on the turn.
Due to villians passive nature, if you cap this flop, check the turn and he still bets, you can confidently fold the river unimproved.
The 1SB invested now can save you 1BB on the river. I cap it.