I've come across a few hands where it's raised preflop and I'm holding A7s. Flop hits me with backdoor flush draw say, (Qh,2S,8c and my suited hand is clubs). Let's say I'm playing middle to late position with three others in hand. Everyone checks and button (who originally raised preflop), bets. If the rest of the players call without raising is this hand worth continuing?
Seems to be a longshot hand, but I've run across it a couple of time and wonder how others play it.

Ya...I was way off. lol.
See below for a better answer.

Prob. of a flush: 4.2% / 22 to 1 odds
Prob. of 2 pair or trips: 1.4% / 70 to 1 odds

Now, lets consider str8s:
1) 2 x OE straight (Ex: you have A7 and flop is 56x; you have 3 consec. to str8)
prob of completing: 3.0% / 32 to 1 odds

2) gutshot to OE str8 draw (Ex: you have A7 and flop is 58x; you need a 6 and then its OE)

prob of completing: 1.5% / 66 to 1 odds

3) 2 x gutshot str8 draw (Ex: you have A7 and flop is 59x; you need a 6 & 8)

prob. of completing: 0.5% / 199 to 1

If I'm not mistaken, you can add these separate probabilities.

Best case example: Assuming 2 pair or better is good:
You have A7s
Flop: 5s6hQs

Prob of flush: 4.2%
Prob of 2 pair or trips: 1.4%
Prob of str8: 3.0%

Total probability of hitting a hand: 8.6% Odds: 11-1
Of course, the probability of getting an Ace (if you think TP is good enough) is 12.5% / 7 to 1 odds

I don't know how to do the math to answer: what are the odds of getting either TP, 2 pair, trips, str8 or flush? Maybe someone else can answer that.