I re-barreled a Martini Cadet to 256 Win and the primers looked as you describe until I reduced the firing pin/hole dia from .105" to .065". The higher pressures were forcing the primer metal into the pin hole and the primers looked flat except for a small "ridge" where some metal flowed into the hole.
If there is any resistance when you drop the lever to extract the fired ctg. this could be the problem except it's hard to believe Browning would make the firing pin hole too large. Take a REAL close look at "flat" primer to make sure there is'nt a small circular ridge of metal where the usual "dimple" should be.
Good luck finding the cause of the problem and when you do be sure to let us know what you found.