lol at the results where do they get these ppl.. I would proly make a note on them after that hand saying something like wide calling ranges and/or bluffed turn into 2 players after being checked to and c/gave up after being called
C-betting on the flop is ok, I guess, as it could make one of them fold. Checking is good also.
I think the clear mistake here is check-folding the turn, giving the opportunity for BTN to bluff!
This is a situation where I like to lead on the turn as an "investigative bet" (doesn't need to be big, maybe around 400-500 chips). If he raises, than you can give him more credit on the flush he is representing. But if he doesn't have the flush, he is most likely folding.