powders don't have a burn rate in the sense of physics ie, units of wt/time -it a burning index. as long as pressure differential exists between the inside of the barrel and the outside pressure the hot gases will push the bullet, the pressure acceleration curve is flat after the first 1/3 of the barrel using either fast or slow powders. if the bullet is pushed to a higher velocity its because that powder simply has more energy in it than (chemical) than another. If you were to choose a "fast" powder that had the same molecular wt. of nitrates as a "slow" powder the bullet velocity would be the same, (although the gun might not be) some powders certainly are more efficient than others than this regard. excessive muzzle flash doesn't add to recoil -- the recoil difference is simply the wt. difference in the exit velocity of the gas mass, not the pressure differential, if a higher recoil is obtained from a flashy powder, the powder wt. was simply higher. Exit pressure can be as high as at least 4x atmos. this is what makes muzzle brakes work (breaks). extruded powder such as Varget and benchmark are pretty much more consistent than ball powders and less temperature sensitive.
An optimized powder (and thus pressure) would be were the derivative of the work curve crosses the velocity deceleration curve using pressure as a baseline in the shortest barrel possible.