Sethix the Swashbuckler has been Swallowed Whole by a T-Rex. In order to help cut his way out, Sethix wants to Feint to gain Panache, since he is a Fencer Swashbuckler. Is this something Sethix can do? I'm aware the flat-footed condition would be redundant, but that's not the point here, perhaps Sethix has Goading Feint, or perhaps he really doesn't care.
Technically, you can attempt to Feint against a creature that has swallowed you
From a pure mechanics standpoint, nothing prevents you from Feinting. Being Swallowed Whole imposes the Grabbed (which imposes Flat-Footed and Immobilized) condition and you are Slowed 1 . Since you're Immobilized, you can't take actions with the Move trait, and attempts to use the Manipulate action have a chance to automatically fail.
To attempt a Feint, you need to be within melee reach of the target, and that's it. The Feint action has neither the Move nor the Manipulate trait, it only has the Mental trait. As part of the Feint, you have to make a Deception check vs the targets Perception DC. This brings up the question of if you can Deceive a creature that can neither see nor hear you, but technically, Feint doesn't actually require that the target can perceive you. As far as I can tell, nothing in the rules actually prevents this, although Perception is referenced in a lot of places, so I may have missed something. So theoretically, you have a chance for success, and there aren't even any actual penalties to the attempt to boot.
That being said, were I the DM, this would automatically fail.
A Feint is an attempt to trick your opponent, by making a false blow or some other distraction, to try to get them to defend a location that you aren't actually attacking, in order to create an opening for you elsewhere. If a creature cannot perceive you, then you can't trick it.