Now I want to respond to the original post. It's been a while and I've had some time to think and play quite a bit more poker.
As always, this post comes with a dose of salt required, as my experience is in micro-limits only.
HOWEVER, that said, a minimum raise of a pot-sized bet on the flop CAN get you to the river cheaply. Many times the original pot better is leading out with a hand that feels strong but vulnerable to him - usually top pair or TPTK. If you pop him back with a minraise on the flop, he will usually stop and think a second, worried about two pair or a set -- and then he will usually call the minraise, and then check to you on the turn.
Obviously, if he re-raises the flop, you're bumming. But if not, your minraise on the flop is much cheaper than having to call his new pot-sized bet on the turn. So that's one advantage.
The second advantage is that he probably puts you on two pair or a set on the flop, and then thinks you're trying to sucker him with a slowplay when you don't bet again on the turn. (The faster the game is moving, the less time he will have to adjust his thinking.) So even when your flush does hit, you're likely to get paid off. You may even get him betting before you on the river to represent that he hit the flush -- since he "knows" you're on a set or two pairs! And when your flush doesn't hit, you have a reasonable chance of inducing a fold on the river.
So the play can work, at least sometimes, at least at some levels. It will never be a standard play the way it is in limit poker, but maybe the fact that it's not standard can make it work for you if you mix it in.