There already is a turret that swipes most FF immune turrets.
Looking at the list of FF immune stuff:
Cutless: Close combat ----> Flak
Eyebot: Refractive --------> Flak
Inflatrator: Swarmer ------> Flak
Spire ram: Heavy ---------> Not flak
Vampire claw: Refractive --> Flak
Raid starship : Refractive -> Flak on paper but not in practice
I'm sure I missed some things, but flak turrets annhilate most FF immune things.
The military command station counters the cutlass and the claw outright with immunity, and it counters the eyebot hard in that it nullifies its cloaking, and the anti missile turret outright stops the eybot. The rest are vulunerable to gravity turrets.
Raid Starships are actually Ultra-Light--assuming that their in-game tooltip is correct. Snipers work best against them, because they have immunity against Radar Dampening, infinite range, and a good bonus against Ultra-Light. And, as you mentioned, Gravity works great against Raid Starships.
Good call on ultra-light instead of refractive, but the end result is the same. Even though the flak cannon gets a bonus to its damage, it still isn't enough to puncture the armor cleanly. although mk II flaks and above do get somewhat through the armor. A sniper free in K and in over twice the cap does more damage then a mk III flak cannon.
Flak cannons are not like the usual turrets in that its not meant to be held far away like other turrets. It's powerful aoe, short range, and high health means it is most effective right in the middle of the ai path, preferably under shields. However, I do think the flak cannon does need a higher cap or a buff. It is already very expensive as far as turrets go, and unless its nature of being forced under turrets and short range means the few you get with its caps make it not give as much "umph". 1v1 I can argue its uses: 1 v 2 it is much harder.
For this reason, the best all round anti ff combo by far is MLRS and lightning turret. MLRS are not as high potential dps as the flag 1v1 in huge waves, but its much higher range and higher caps make it much more flexible and effective, and it gives drones for enclaves to boot. MLRS cream all but the refractive hull type, and the lightning absolutely, positively melts the numerous but individually frail eyebots.