Yes, you can purchase one with military letterhead if your commander will write it up. That's a big IF. The problem is that legally the gun still belongs to Uncle Sam when you leave service. If you were a cop on the other hand, it can become yours at retirement.
§ 922(v)(1) It shall be unlawful for a person to manufacture, transfer, or possess a semiautomatic assault weapon.......
(4) Paragraph (1) shall not apply to -
(A) the manufacture for, transfer to, or possession by the United States or a department or agency of the United States or a State or a department, agency, or political subdivision of a State, or a transfer to or possession by a law enforcement officer employed by such an entity for purposes of law enforcement (whether on or off duty);
(C) the possession, by an individual who is retired from service with a law enforcement agency and is not otherwise prohibited form receiving a firearm, of a semiautomatic assault weapon transferred to the individual by the agency upon such retirement; or.....
Become a cop, get it letterheaded that way, and retire down the line to keep your gun.
[url]http://www.atf.treas.gov/firearms/legal/semi.htm[/url]