He is right. Flpping 4 diamonds (or any suit) to the flush leaves 9 outs (13 in a suit - 2 in ur hand - 2 on board = 9)

Leaving 2 cards - the turn and river- yet to be displayed, he does have a 1/3 chance of hitting a diamond at that point. I the turn was no diamond, then he would have less chance (im not sure chances at this point). But yeah he had 1/3 chance.

This being said- that kid was pretty lucky- u got a bad beat-
pot odds dictated that he had to pay 15.95 - ur bet- to win (16 + 4 + 8) = $30. he was gettin rough 2 to 1 payout and had 1/3 chance to win. Bad move but luck forgave him. Hope I helped

Edit: most books on holdem (at borders, library?) can give u basics like this. I recommend the book of bluffs later on its pretty good.