$2.10 Turbo HU Push AI with weak flush draw?

Check-shove is bad. It pretty much look exactly like what you have, a draw. So check-raise to 180 would be better than shove. Problem versus decent thinking player is that you likely have quite few strong made hands that should be check-raising here. 33, QQ+, KT+ you would likely raise or shove preflop, right? Qx check-raise would not make sense. So what you are check-raising is K3, Q3, maybe some K8 and draws. That board offers lot of draws so your check-raise tends to be draw heavy.

So for those reasons I would prefer to check-call or lead flop. You might e.g. check-call flop, check turn and if he checks behind bet river whatever you have improved or not.