I don't think the flaw is in the Constitution. I think the flaw is in letting irresponsible idiots have guns. The assholes running the NRA are wholly owned by the gun makers, and the gun makers are using their propaganda arm - the NRA - to convince people that anyone capable of holding a gun is magically entitled to do so, and magically entitled to shoot anyone they want.
The money-hungry people running the NRA shoot down any attempt to slow the flow of cash. Thus, there are - for practical purposes - no competency requirements for owning a gun, no knowledge of the law requirements, no tracking requirements, and really very few restrictions on transfer of property. Oh, sure, you hear people bitch about how hard it is to sell a gun to a relative, because there is a form to file, but shit, there are more forms for transfer of cars or houses, and no one whines and moans to the same degree that their rights to sell cars are being impeded by inconvenient paperwork.
There are many responsible gun owners. The problem is that a gun can kill in an instant, and letting irresponsible people carry them means everyone around those people is suddenly at risk of instant death.
Thus, the meme. Where does my right to not be instantly killed by some asshole start, and where does some asshole's right to instantly kill me end?
We're talking about the guy who can't get into a parking lot, and decides he needs to shoot people.
We're talking about the asshole who decides he has "road rage" and starts shooting.
We're talking about George Zimmerman, who hunted down and assaulted a kid and then killed him "in self-defense."
It's not the mentally ill or the terminally criminal we're worried about. It's the "Joe the Plumber" types who do not value human life, and will irresponsibly whip out their can-kill-in-an-instant devices when they get pissed off.
Think the root problem is a mindset that shooting people is acceptable behavior. A serious lack of grasp of consequences, as lack of respect for human life, and idiots with devices that can kill in an instant.
Some of these are accidents (shooting the kid downstairs), some of them are assholes with a hard-on (vigilante-style shooting at shoplifters? Seriously?). Some of them are just insane (shot the neighbor girl for not letting him/her pet the dog? He was probably a child himself, at the time, but are you fucking kidding me?).