Brock has reportedly struggled with mental illness and been hospitalized for it. He allegedly believes he is being targeted by right-wing assassins. If he is a prohibited person, it would be a felony for him to purchase or even possess a firearm, and possibly a felony for him to be guarded by an armed bodyguard (due to laws intended to prosecute mafia dons -- I don't have the link for this handy).
Brock allegedly armed his assistant with a Glock handgun purchased in Maryland. This is arguably a straw purchase, which would be a felony.
The assistant allegedly carried the firearm within Washington, DC without a concealed-carry license. DC does issue concealed-carry licenses for professional security guards, so this could have been legal, except that the paperwork was not done. Without the paperwork, it's a felony.
The Glock handgun allegedly purchased has a 17-round magazine, which is forbidden by DC law (which has a 10-round limit).
Without a registered firearm, possessing ammunition is a felony in DC.
And, of course, any travel out of the area could run afoul of concealed-carry laws in other states, depending on where and whether the aide was licensed in that state.
This is just another David Gregory case: the gun control laws the left so desperately demands aren't supposed to apply to them.