So I was playing a game this weekend with my friend, he was playing a Revenge Squad deck.

During one of my attacks, I played a Flying Kick. As a response, he flips Imprisoned in the Source and names Flying Kick as I had played a Flying Kick during a previous attack.

How does this resolve?

I am of the belief that Flying Kick has already been "played" and it's effect is in the chain, not the plot twist. Which is why cards like Fizzle specify that you are negating a plot twist effect.

His belief of course is that he could flip Imprisoned in the Source and my Flying Kick would be fizzled.

Who wins this one?

You are correct. The plot twist has already been played so he cannot prevent you from playing it. It doesn't negate any effects, it just prevents someone from playing a particular card.

IitS can only stop plots from being played, it doesn't negate them once they're already on the chain. You flip IitS, the opponent gets a chance to respond and play any plots he wants, and then when everything resolves, the IitS's owner chooses a plot name, and from that point on it can't be freshly played.

Wow, thanks for the super fast reply!

I'm also glad to see that I was correct in my reasoning.