d o u b l e . j e o p a r d y
Remember, George Zimmerman was investigated by DOJ after his Florida acquittal. IIRC, it was for allegedly violating a federal housing law against "... using force or threat of force to interfere with a person’s federally protected housing rights on account of that person’s race or color.”
Ultimately, DOJ admitted that it had nothing on George, so the investigation ended without charges being filed. God only knows what sort of nonsense they'll cook up to go after Kyle.
No Federal and State are separate and it is not double jeopardy.
That said, there isn’t any thing to charge him with federally.