if you get Ah,8h, 2h,
then how big the chance you can make a flush?

1 out 5???

if it is 1 out 5, then how come it is profitable to paly such hand?

I'm not sure what the exact odds are, but the odds of flopping a set in NLHE is about 7:1, and yet sets are some of the most profitable hands to make.

Its called implied odds. You lose very little when you don't make a flush, and you win big pots when you make one.

You are actually allowed to hit other cards besides your flush cards, that might help your hand. Also you can outplay your adversaries on later streets and win a pot without showdown.

And mathematically it makes a flush 1 out of 5, but you are not taking the hand to the river every time you play it, mostly you are folding 4th/5th, investing small amounts when you miss and getting a lot back when you hit. After you hit your 4th flushcard on 4th, assuming no information of other cards, you are almost 50% to get there by the river.

Therefore, its profitable...

While you can never be sure that the implied odds are there in holdem, you can almost always be sure they are there in 7CS, especially in multi-way pots as a lot of hands will be taken to the river.

This should answer your question: http://www.math.sfu.ca/~alspach/comp24/