Yes, as long as you don't arm it with a "prohibited" weapon. Even an M2 heavy machine gun could be legal, if you'd done all the proper paperwork to acquire it, including paying the "stamp tax". But you could "look" just like those guys, and maybe be just like them, if you had AR-15s or clones, rather than M-16s. (from the pictures we can't tell if they had AR-15s or M-16s.
(Technically an M-16, made by Colt, is an AR-15, that being Colts designation. But in "the vernacular" AR-15 generally refers to semi-auto only versions, while M-16s are either full auto or burst fire capable. I used the vernacular).
But the rest, the M113 itself, the Kevlar "Fritz" type helmets, the black suits (I'd choose something more appropriate for the region you intended to operate in, like "desert" cammo, even the old "chocolate chip" variety, or more modern ACU/ABU (Air Force type) "digital" cammo), etc. are all perfectly legal for you to own. Not cheap, but legal.
We couldn’t afford all the fancy equipment, but could get Army Surplus clothes and wear our ATV helmets. We are going to look so good on TV- just wait you will see. We will likely carry our 30-80 year old deer rifles, but the media and most folks won’t know the difference. We’ll paint jackrabbits on the side for our kill trophies.
We’ll be the Redneck version of a modern SWAT team. Those of you that can tell the difference in all the equipment will be ROTFLYAO.