I have taken a number of carbine classes and during the night shoots, time was given to see the flash signature of each weapon. At all of them there were a good mix of people using flash suppressors, muzzle brakes, and bare muzzles. In one class, the instructor fired these individual weapons in front of the class both into the side berms and into the backstop so we could see the flash from both the sides and the rear. In another class, each person just told what muzzle device if any they had and then fired a couple rounds while everyone watched. In that class, all shots were fired at pretty much a 90 degree angle to the viewer. All of the weapons were AR15s.
The Phantom and Vortex flash suppressors produced almost no visible muzzle signature as viewed from the sides and the rear.
The various muzzle brakes had significantly more flash than a flash suppressor, but far less than a bare muzzle.
The bare muzzle produced a huge fireball several feet in diameter.
Based on these experiences, I would definitely NOT say that a muzzle brake increases the muzzle flash. Based on my own experiences, a muzzle brake does significantly decrese muzzle climb.