The conspiracy doesn't have to be complicated. And it wasn't. To whit:
You have some low level people making a few bucks snitching, etc. for the good of the nation. They act like they're one thing [Marxists] but are something else [ex military, etc.]. Very similar to how Donald Trump became a paid agent of Russia today but will occasionally spout anti-Russia stuff just to keep things on the level.
Presidents used to ride in open cars with no problem. Look it up - Eisenhower, Truman, Kennedy. Perfect advantage to a cross fire.
You know - on the QT - the president is traveling to Dallas. Perfect. Scout the area, create a fake sniper's nest, plant the fake gun, etc. Not hard to do.
Have your shooters practice in an undisclosed location.
The day comes, the guy taking the fall works in the fake sniper's nest building, the car comes down the street, they stick their guns out and fire [one from Dal-Tex] one from somewhere on the knoll, the deed is done. Perfect.
From there, it's easy to control the message. The Dallas police can easily be manipulated. You got the patsy going to his rooming house [how in the world could a guy making a buck 25 an hour afford to live with his wife and kids AND afford a rooming house too? Uh huh, sure].
Get him to go to the theater to "wait." Gun down a police officer and then "lead" the cops to the theater. Perfect...but not quite. Somewhere along the way, he's not murdered too during a possible shootout.
He starts spouting things when he knows the jig is up. Time to go. Let his murderer waltz right into the garage and he guns him down.
From there, it's pretty much media manipulation of the story, putting on the big show in DC, etc. Pretty much how it's going on in DC today - manipulating the MAGATs in the news.
Not too hard to do.