Chewie has a damage. Rolls for r2dr, gets a hit, flips a card that is a pilot trait. Does determination remove that card all together?

No, as Determination says when you are DEALT a damage card. Flipping it is not affected by Determination.

And Chewie's ability doesn't get to flip it back over again either. Same reason, they only work when being DEALT cards and not manipulating card you already have.