I think you are confusing non-violence, practiced by Quakers and such, with non-aggression of the type advocated by MLK....I repeat: IMO MLK's gun permit would have been inconsequential...yep, whether granted or not.
He owned guns for a reason. Quakers don't for a different reason.
He applied for a permit for a reason. Your suggestion that the racist denial of it was inconsequential suggests he had no reason and really didn't care if the government discriminated against him based on his race. I think his whole life demonstrates the opposite.