Ejumacate a furriner here. 
As I understand it, the US military has its own set of lawyers. Have any of these risen to the US Supreme Court? Is there a bar on appointing them?
There’s no bar to appointing a military lawyer to the Supreme Court (in fact there’s no actual requirement that they be a lawyer at all, though for practical purposes a non-lawyer would never get approved by the Senate in modern times.) The officer in question would have to resign his commission before serving on the court, since federal law prohibits people from working for two branches of the government at the same time.
I don’t know if any JAG officer has been appointed to the Supreme Court, but several have become federal judges in lower courts.
Military lawyers are divided up between two categories - civilian attorneys for the Department of Defense and individual services (Army, Navy, Marine Corps, Air Force) and judge advocates. Judge advocates are uniformed officers serving in a military service who are also licensed attorneys.
Felix Frankfurter, before becoming an associate supreme court justice, was appointed Judge Advocate General for the entire War Department during World War I. Other supreme court justices served in the US military prior (often quite a bit prior) to becoming a supreme court justice.
Active duty military members are forbidden from campaigning for political office or holding any elected office or office appointed by the president and requiring the advice/consent of the Senate. So it may be potentially feasible that a national guard judge advocate not on Title 10 status (triggering statute that transfers powers and authority over a member of a state national guard to the federal government) may become a supreme court justice. But not likely, given all the potential conflicts of interest, both state and federal, that could arise and would require the individual to have to recuse him/herself.
John Paul Stevens, the justice who is about to retire, is one of these. In fact he’s the last WWII veteran to sit on the court. He was in the Navy from 1942 to 1945, and was appointed to the court in 1975.
But he wasn’t a lawyer when in the military. He was an intelligence officer.