What size games are you playing man? I know for a fact that 1 flak per every strikecraft squadron will do the trick. Flak being too good against fighters is one of the biggest complaints the online community has.
Repulse is currently broken. There is no hard counter for any race sadly. I don't want to sound like a jerk, but countering fighters shouldn't be that hard. As long as your flak are staying near your fleet (when they run off they do you no good), you should be taking them out. The only thing fighters are good against is Assailants, Scouts, colony frigs, and bombers.
The fighter ball is more difficult with Vasari, yes, because they don't have an anti-strikecraft damage dealing ability, but flak vs. fighters is a pretty lopsided fight in any given situation.
The best answer I can think of now is to give an example.
If he jumps into the system with say 15 advent carriers with 45 fighter squadrons (which is a lot...if ur seeing more than this ur playing some pretty big games where the two of you didn't start close to each other), I'd have:
1. Space Egg w/ nanite disassembler and gravity bomb (probably level 4 or 5 by this point)
2. Kortul Devastator, probably lvl 1,2, or 3. Depends on how recently I made it, jam weapons of course
3. I'd have probably 40 ish flak. I don't want to make too much flak, but if he's abusing fighters, then you abuse flak.
4. Accompanying them I'll have something in the order of either: a starbase prepped to be made, 10-15 assailants for bait, HC's, Light Frigs....mind you only one of these things. Can't afford all of that so early.
5. The trick would be to jump in all together (you can right click on the jump function of a fleet to make it do a group jump). Once you jump in together, have the fleet set to close proximity so the flak won't go wandering. Wait for teh fighters to get close, then micro hit jam weapons. Boom. He'll lose at least 10% of his fighter strength (I think 25% might be more accurate) on his first pass and not do a bit of damage thanks to jam weapons.
6. If he's smart enough to stay away (which it sounds like he probably wouldn't, but he may, who knows), then build a starbase to take the contested system. He'll either fail to take out the starbase cause fighters are awful against buildings, or fail because he'll try to send bombers meaning he'll scrap his fighters and send bombers in piecemeal to be chewed up by ur flak.
Again, that's just a guess as to what situations ur seeing.
ONE MORE THING
This is a slim possibility. I haven't used jam weapons since the beta was released for entrenchment. This is because once upon a time, Jam weapons wasn't programmed right and didn't work....at all. It's possible this was never fixed so jam weapons isn't doing anything.