If we’re talking the actual NeoGeo versions rather than ports, let’s see…
In the KOF series, there’s 98, 99, and 2000–those let you turn the red screen flashes off (“Flash” option; they put that in after that Pokemon episode with flashing red/blue or whatever gave 300-some Japanese kids seizures in 1997–I mean, I don’t know for sure that was the reason, but it’s quite a coincidence!), and let you turn the super moves (“Power Gauge”) off; most supers have white/black screen flashes. '98 still has screen elements that give off their own little flashes as they draw in; '99 has small flashes there and there, like in screen and stage transitions, and lighting flashes through the windows in the museum stage. Mostly I play 2000. : )
The early games in the Art of Fighting (1 and 2 at least), Fatal Fury (1, Special, 2), and World Heroes (1) series don’t have big flashes as far as I remember. They do have big flickering shadows under the characters, and no power meters or anything down there to hide them, so those can be a bit eyeball-irritating.
Garou: Mark of the Wolves has a lot of fancy effects, but they were more subtle with the animations by that time so they aren’t too bad for the most part as far as flashing goes.
Karnov’s Revenge might be okay, I’m not familiar enough with it to vouch for it entirely, though.
That’s about it I think, although I may be overlooking a few of the more obscure ones.