[pudley4]

The easiest way is to figure out the chance that he doesn't hit the flush, then subtract from 1 to find the chance he does.

7 total cards known, 45 remaining. 6 flush cards known, 7 remaining.

Probability of not hitting on the turn= 38/45.
Probability of not hitting on the river= 37/44.

Multiply these together to get 1406/1980.
Subtract from 1 to get 574/1980=.28989.... So he has a 28.9898% chance of hitting the flush by the river.

To figure out the odds, it's 1406 to 574 against him hitting=2.449 to 1 against.