I've had that exact same issue. For me it was the Winchester primers in that 350 FMJ ammo. Try a different brand of ammo to see if the issue persists. I can usually get the ammo to fire on a 2nd or 3rd attempt, but mostly I quit buying that ammo because it sucks and my partner reloads ours anyway.
If that's the only ammo available to you, I recommend shooting it in a lower with a stronger hammer spring. The 350 legend AR I hunt with has a single stage CMC trigger, and I use either Hornady interlocks or similar handloads. Good luck.