[jason1990]

The probability player 1 was dealt two suited cards that match the suit on the board is

p_1 = (10*9)/(47*46).

The probability that player 1 AND player 2 were dealt two suited cards that match the suit on the board is

p_2 = (10*9*8*7)/(47*46*45*44).

We can continue until p_5, but p_6 and beyond are all 0 since at most five players can flop a flush. So, by inclusion-exclusion, the probability that at least one player flopped a flush is given by the following formula, in which xCy denotes x!/(y!*(x-y)!):

sum_{n=1}^5 { (-1)^{n+1}(9Cn)p_n }.

Using this, I get that the probability someone flopped a flush is about 33.3%.