bet turn, otherwise wp
vs normal calling ranges, he isn't going to have many combos of draws, he will most likely have Ax and other middle cards under the KK, with our hand being basically unbeatable on the flop, i think checking is the best option since if we bet the flop we are rarely going to get any action at all in most situations.
So i like the flop check, but i don't like the turn check, even though it basically changes nothing, by the turn we have to try and get some chips in there, or just take the pot now, also with the 3 it gives him the chance (albeit low one) of pairing that card, but also it may give him a bunch more combos of outs with draws, so we will want to bet to protect as well and we're not worried about taking the pot on the turn either, since it's so unlikely that he will hit a card on the river.
Don't beat yourself up about it, he just happened to have a draw on the flop and happened to hit a 3 outer to beat you, it will happen, but if you bet the flop here, he will likely call with his draw leading to a very similar result on the turn anyways, Keeping things really simple in
freerolls is a really good idea, so getting it all in with two pair or better is pretty much a must on most boards without obvious draws being completed. So it wasn't really that bad of a play, i bet in game you were pretty happy to call his all in jam on the turn.
Lastly, try to leave out villians
hands in all future hands you post, otherwise you will get some very skewed/bad answers.