My question is: does Determination work on Chewie flying a Falcon? Chewies pilot trait says he flips face up damage cards dealt to him face down, but Determination lets tou discard face up damage cards with the pilot trait. so which triggers first? The determination or Chewie?

You get to choose the order they will resolve.

To put it simply if you are dealt a Face-up card to Chewie w/ Determination you can first have Determination look at the card, and if it is a pilot card DISCARD it, before it gets to Chewie who looks at it and then flips it over. Now if you REALLY want to take the damage that Determination could prevent you should be able to use Chewie's ability first which means no face-up card for Determination to look at.

My question is: does Determination work on Chewie flying a Falcon? Chewies pilot trait says he flips face up damage cards dealt to him face down, but Determination lets tou discard face up damage cards with the pilot trait. so which triggers first? The determination or Chewie?

As the controller of two effects that trigger at the same time, you get to decide the order in which they resolve. Unless the player controlling him is up to something wacky, Chewie with Determination will discard all pilot crits and turn the rest face down without resolving them.

Thanks for clearing that up!