Being serious about it for a moment, it's extremely unlikely that it's a false flag attack. It's fun to joke about the idea, but the reality is that it doesn't appear to be staged, and he's far too much of a coward to agree to have somebody shoot at him.
Besides that, there's plenty of politically-unaffiliated groups or individuals who would probably want him gone just for how his last term contributed to the abortion bans, reunification of church and state (in some states), government corruption, etc.
No one needs to actually shoot at him, he can just have a capsule of fake blood in his hand and smear it on himself at the right moment. It's so easy even he can do it.