Situation: A player draws a face-up Thrust Control Fire damage card (Receive 1 stress token, then flip this card facedown).

Question: Does a face-up damage card that instructs you to flip it facedown after resolution prevent Boba Fett crew trigger?

The face-up damage card was "dealt" so it seems Boba Fett requirements are met and the player also suffers any effect from the faceup card also. Is there any timing conflict that prevents resolution of one or the other?

You answered your own question. The defender is dealt a card face-up, even if it is discarded, flipped face down, or otherwise no longer face up for whatever reason. Therefore, Boba Fett procs.

As mentioned it is all about being dealt the card face-up.

Now I do think that Draw Their Fire CAN stop Boba from triggering. This would happen because while the target may be target "hit" by the attack the face-up card is going somewhere other than to the target. Only the DEFENDER needs to worry about Boba and only if it is the ship being dealt the face-up card.

Yeah, Draw Their Fire would block Boba if it was the only [kaboom] being suffered, you're quite right. As would Xizor's ability.

Hmm, does that mean that Chewbacca could be affected by Boba? He always flips the face up cards he gets but technically speaking, he IS dealt face up cards.

Hmm, does that mean that Chewbacca could be affected by Boba? He always flips the face up cards he gets but technically speaking, he IS dealt face up cards.

Exactly. Does not matter what effect flips the card facedown, as long as it is dealt faceup, Boba triggers.

Hmm, does that mean that Chewbacca could be affected by Boba? He always flips the face up cards he gets but technically speaking, he IS dealt face up cards.

Most certainly. It also means that even if Determination or some other effect IMMEDIATELY gets rid of the face-up card it was still dealt and Boba would still trigger.