Assume there are 2 suited cards on the flop. If he has 2 pair with the 2 suited cards, then you have 9 outs. If he has 2 pair with the unsuited card, then you only have 8 outs since one will fill him up or he has it in his hand. Assuming you have the full 9 outs, then the probability that you hit your hand by the river is actually 36.4% rather than 35% since there are only 45 unknown cards instead of 47 since you know he doesn't have one of your suit. 1-(36/45)(35/44) = 36.4%. Now the probability that you hit your hand on the turn and he hits his hand on the river is the product of these two probabilities which is (9/45)*(4/44) = 3.3%. Then the probability that he hits on the turn and you hit on the river is also 1.8% This probability is only significant if you won't be able to get away from your hand if he hits on the turn. 36.4% -1.8% - 1.8% = 32.8% for the chance of hitting your flush and winning.
You can also compute this with poker software. Using
www.twodimes.net/poker gives 33.13%. The small difference is due to the possibility of the flush draw making trips.
<pre><font class="small">code:</font><hr>
Running: pokenum -h kc 6c - ah 9h -- ac 9c 2d :
Holdem Hi: 990 enumerated boards containing Ac 9c 2d
cards win %win lose %lose tie %tie EV
Kc 6c 328 33.13 662 66.87 0 0.00 0.331
Ah 9h 662 66.87 328 33.13 0 0.00 0.669
</pre><hr>