You can put this solution on YOUR website! A flush says all 5 cards are the same suit.
No matter what card you pick for the first card, you are ok.
Now the second card has to be the same suit. There are 51 cards left in the deck and only 12 of the same suit as the first card. for the third card for the fourth card } for the last one
So the odds of a flush are
If you look up the odds for flush with a web search, you will find a lower number. But those guys make a distinction between a "flush" and a straight flush and a royal flush. But a flush is a flush, so i am sticking with the higher number