[junk2drive]

The Brigade commander was a Brit.
From the link above:
"This force was built around the British 27 Commonwealth Brigade which, at the time, consisted of a battalion from the Royal Australian Regiment, a battalion from the Argyle and Sutherland Regiment, and a battalion from the Middlesex Regiment. Since these infantry battalions were without supporting arms or services of their own, Eighth Army attached to the brigade U.S. artillery units, engineers, and the 89th Medium Tank Battalion. This combined force, commanded by Brig. B. A. Coad of the British Army, was under the operational control of the 1st Cavalry Division, but worked as a separate task force at a considerable distance from, and without physical contact with, that division or other friendly units."
I made a version of this battle for CMAK and the same thing happens there for the country flag, but not the individual units.