I think you'll be fine if you keep the camera more than five or six feet away. The flash won't be that bright since smokeless powder just doesn't get that hot. It's light is mostly infrared and most cameras have an infrared blocking filter. The visible portion of the muzzle flash is a pale yellowish.
The sound overpressure could rupture the microphone's diaphragm if the camera is closer too. Something solid like a bit of sticky tape over the microphone holes will help protect it if you need to get closer.
The main risk is contamination by the powder residue. You don't want that collecting on the lens or the internal works. An underwater housing will give great protection from that. Or you can enclose the camera in a plastic bag with just the lens exposed. Try to find a cheap ultraviolet blocking filter for your lens. Much better to sacrifice that than the whole camera.
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