The late Kurt Vonnegut, Jr., was a gifted author. He had also the misfortune of living through one of the single most destructive acts in the history of mankind, the Allied bombing of the historic German city of Dresden in the waning days of World War II. That attack killed more Germans than the number of Japanese killed in either of the two atomic bombings of Hiroshima and Nagasaki later that same year. That experience, and the relative scales of carnage, heavily influenced Vonnegut, who was an American prisoner-of-war being held in Dresden at the moment of the firebombing of that city. Which brings us to the character of Bertram Rumfoord. Rumfoord is introduced to the reader in Chapter Five as the roommate of Billy Pilgrim while both recuperated from separated events in a hospital. More importantly, Rumfoord is described as "the official Historian of the United States Air Force," the branch of the armed forces that, obviously, carried out strategic bombings of enemy cities throughout the course of the war (at the time of the war, the Air Force was part of the U.S. Army and was designated the U.S. Army Air Corps. After the war, the Air Force was created as an independent branch of the military).
Bertram Rumfoord is reintroduced the reader in Chapter Six, where he serves as a literary device, albeit a highly entertaining one, to enable Vonnegut to reemphasize his central theme about the scale of destruction rendered upon the city of Dresden. As the official Historian of the Air Force, Rumfoord would logically have need of the material Vonnegut wants to include in his novel, especially the verbatim transcript of President Truman's announcement of the atomic bombing of Hiroshima. Truman's announcement provided the destructive power of the atomic bomb, and the justification for its use. Vonnegut, however, isn't interested in the destruction of Hiroshima. He is interested in illuminating for his readers the destruction of Dresden, about which most Americans knew little and cared less. That is why he has Rumfoord's hapless wife Lily bring from the library to the hospital room that Bertam shared with Billy Pilgrim not only the Truman statement, but The Destruction of Dresden by David Irving, a British author who, years later, would become known for his efforts at exonerating Nazi Germany for the Holocaust while portraying the Allies as the real force of evil during World War II.
All of this may or may not be relevant to the matter at hand, in effect, whether General Rumfoord is a "flat character." To the extent that a "flat character" is defined as a two-dimensional figure who remains fixed as a somewhat superficial character, then Rumfoord is, indeed, a flat character. The following, from Chapter Six, is the biographical detail Vonnegut provides for this character:
"Rumfoord was a retired brigadier general in the Air Force Reserve, the official Air Force Historian, a fun professor, the author of twenty-six books, a multimillionaire since birth, and one of the great competitive sailors of all time. His most popular book was about sex and strenuous athletics for men over sixty-five."
And, he is on his fifth wife, a much younger woman of limited intellectual capacity, and is dismissive of Billy, declaring that "'All he does in his sleep is quit and surrender and apologize and ask to be left alone'." Rumfoord exists solely as a plot devise to introduce supporting material for Vonnegut's main thesis regarding the bombing of Dresden. He is entirely "flat."