It's easier if you try to figure out how often you *won't* hit your flush. On the turn, 38 cards can fall that are not your flush cards. The river has 37 of those cards (since we're assuming one already fell on the turn).

Chance(miss) = (38/47) * (37/46) * 100 = 65.03%
Chance(hit) = 100 - 65.03 = 34.97%