According to the lightgun patents, the screen MUST flash so it can find out where it's pointing at.
I'm not sure if all lightguns work according to that patents, but I don't remember a single lightgun game EVER that didn't flash when you shoot. When the screen flashes white, the gun waits for light intensity changes at the point it's aiming at. Since the TV has a fixed refresh rate, it's possible to calculate the approximate screen position for a pixel based on how long it took to fill it with a different color.
There are games that show a target where you're aiming at (Jurassic Park, Gun Blade NY). I have no idea how that works.