3 of a Kind beating Flush by river?

Hello, what are the chances of beating a flush when you have 3 of a kind on the flop, by the river? Thanks

You've got 7 outs on the turn, and, failing that 10 outs on the river.
Thus, the chance that you will not make a full house or four of a kind by the river is
40/47*36/46=1440/2162
then the cance of hitting is 722/2162 - just a hair over 1/3.

Notably, some three-of-a-kind hands can also make flushes or straight flushes on the river, but I ignored that.