I would usually lead the flop myself but I appreciate that has zero fold equity in this exact hand while a check raise can actually pick up the pot immediately and stands the best chance of getting stacks in if the flush hits. Either way I'm almost always playing my flush draws fast as they are too obvious when they come in otherwise. The alternative route of disguising your nut hand leads to tiny pots on the river and potentially bad cards like board pairs or a fourth flush card falling. Boards usually get more threatening so if they are too afraid to call the turn they are unlikely to find the courage to call the river without hitting something. Therfore as played I bet the turn and quite big hoping it looks bluffy.
The one time I've slow played a flush recently was when I flopped the nuts on the button after calling a raise while shorthanded. The pot was three way on a very low monotone flop with my kicker blocking straight draws
. Neither opponent looked enthused so I checked it back. Same disinterest on a low card turn that put various low straights on board, so I checked it back again.
River is another connected card but higher. Finally the original raiser over bets the pot. I estimate he has a range of [straights]. I shove on him and win nut flush over rivered nut straight. Sad cooler for him but fact is I knew he had nothing he was happy with till he told me so on the river. I knew how to play the hand perfectly because I was in position and I'm good at reading players' enthusiasm for their hands.
OOP on a double Broadway board with multiple mid card straight draws and vs a loose player I'm just coming out betting with my big hands. I can't get as much info OOP nor do I have the option to bet any street my opponents refuse to. That makes slow plays OOP dramatically less profitable than IP.