? are they both neutered?

You might buy a Feliway diffuser and use it in the main room to help
destress him. I'm certain he will get past it and like her again. Give him
LOTS of extra attention in front of the kitten so he cannot mistake that he
is being 'replaced' but rather just added too. He might be eating too fast
thinking the kitten will get his food. Does he eat wet or dry?

If vet checked him out & he's OK, sounds like he's jealous--I agree, he may
be eating up all his food--kittens just have a way of getting into
everybocy's food bowl and eating away-just has to happen once and he figures
he'd better eat it all up real quick...  He's probably a little mad, hence
staying away from everybody...  A couple of tricks sometimes work-put some
real smelly hand lotion/bodylotion/etc on both their noses--now they both
smell the same thing & the same way...  Make sure he has a a place,
preferably off the ground, that the kitten can't get to--he'll love to just
watch her try to jump up!  Also, kittens have a lot more energy and she may
just be tiring him out.  I once fostered a kitten who singled out one of my
cats to be his best buddy--drove him crazy, followed him around, 'attacked'
him (kitten play fighting), ate his food, etc.  He would play for a while
and then jump up somewhere kitten couldn't get to!  Finally, I don't know
how old kitten is but until she's spayed she may be giving off scents he's
just uncomfortable with...  Give him lots of attention; use treats, toys,
etc & my guess is that they'll turn into best buddies.  One last thing,
throwing up may be sign of hairballs--have you tried giving him something
like Petromalt--works wonders.