A muzzle brake is specifically intended to reduce recoil. Any reduction in flash is mostly incidental to the designed purpose.
A flash hider in the "old days" was simply a cone-shaped attachment. You can see pictures of this style on older machine guns and some of the 20mm "anti-tank" guns of the past. It was intended to reduce the shoter's loss of night vision, primarily, rather than hide the flash from an enemy.
These Klintonista laws make things somewhat confusing, but any gun not banned on account of bayonet lugs and flash hiders and wrong colored paint or what-the-hell-ever can be shot with a flash-hider attached. If not, I've obviously missed something...
FWIW, Art