[AaronBrown]

As Thinkquick and several others pointed out, you have to account for both the spades and non-spades among the other pocket cards. If you do it correctly, you get exactly the same answer.

The usual calculation is to say there are 9 spades among the 47 unseen cards. The chance of getting a non-spade on the turn is 38/47, and if that happens, the chance of getting a non-spade on the river is 37/46. Multiply them together and get 1,406/2,162. This is your chance of not getting a flush. Subtract from 1 to get the chance of a flush, it's 756/2,162 = 34.97%.

To do it your way, you have to consider how many spades are in the other players' hands. The table below shows the possible numbers of spades from 0 to 9, the probability of that many spades being in the other players' hands and your chance of making the flush given that many spades in the other players' hands.

0 0.735% 53%
1 5.670% 48%
2 17.525% 43%
3 28.446% 38%
4 26.668% 32%
5 14.934% 26%
6 4.978% 20%
7 0.948% 14%
8 0.093% 7%
9 0.004% 0%

If you multiply the last two columns together and add them up, you get exactly the same 756/2,162 = 34.97% as the standard calculation. Doing it your way is handy for some purposes, but unless one of those applies, it's a longer way to get to the same result.