Since in this hand the second spade hits on the turn, the chances that one our opponent is chasing the flush is lower. With this in mind, we are pretty much against made hands, but pretty weak made hands since they have checked on the flop and called and are now checking the turn. I might take the free card here, since betting doesn't disguise our hand more: our opponents won't suspect we are on a flush draw with no pair at this point. The best card that could come out is a spade card that pairs the board since our opponent will catch up and the probability of them having two pair right now is slim given their actions.
Betting would be good if the two callers called and we don't face a reraise, but this would be the perfect scenario. If one of them raises and the other one folds, we face a difficult situation, since pretty much only our A and the spade draw are our outs, wich figures out at:
4 + 9 = 13, but we cannot be sure that our A is an out since A-10 could checkraise, heck, even AK or A3 could raise in that spot if we follow our read (agressive players). With 3 1/2 + 1 1/2 SB = 2.5BB in the pot, this is pretty dry since if we get raised by the SB and BB folds, we'll invest 2BB in a 6.5BB pot, not quite getting the ratio we need to call the raise.
But if we are pretty sure we'll only get called, or that a the raise will get a caller (you and another guy) betting is a better option than checking since we'll build the pot and still get good odds
to play our flush (and probably get payed nicely if we hit). I probably bet here, since I also have the possibility of taking the hand right here.
The chances that someone right now has a flush are high given the check call on the flop and now the check. In this spot, we are a lot more likely to get checkraised and if we do, we are much more likely to go heads-up, giving us worse or even incorrect odds like we saw in scenario one (we bet, get CR, BB folds).
I take a free one everytime here:
a) We haven't invested much in the pot and it is small (we are 3 to 1 on our money)
b) We are likely to get C/R
c) We get to keep our BB and fold if we don't hit anything (and I'll probably check if an Ace hits and it is checked to me).
d) We will get at least 1BB if we hit and two if someone doesn't believe us. I've even seen people cap with a low flush a 4 suited board before....
e) We are pretty unlikely to get somone to fold, especially if they're in the same boat as us.