Use the turn and river odds if:
A. There will be no more betting after the flop. For example: your opponent goes all-in on the flop and your call closes the action. You're guaranteed to see both the turn and river.
B. Stacks are deep and you're getting good implied odds. Implied odds are future bets you think your opponent will make after your out hits. So, if you hit the flush on the turn and you're positive your opponent will bet out on the turn and river, then you have the implied odds to call. If you think they won't bet when a 3rd flush card hits and you can't extract anymore money from them, then you don't have implied odds and it's a fold. Look up implied odds and reverse implied odds for more information.
You would use the flop to turn odds when there is a chance at future bets, but aren't getting the implied odds to call. So, use this more when stacks aren't as deep. So, if the pot is 10BBs, effective stacks are 25BBs, and your opponent bets out 10BBs, you have to call 10BBs to win 20BBs. You aren't getting the odds to call. And if you do, your opponent only has 15BBs behind, so they're likely betting 15BBs on the turn to which you have to call15BBs to win 45BBs. Again, imperfect incorrect odds to call.