The show takes place from 1865 to 1867, yet the fort flag has 37 stars on it. But the 37th state (Nebraska) wasn't admitted to the Union until Friday, March 1, 1867, so the number is incorrect for most of the series.
James Hampton's character, Bugler Hannibal Dobbs, is a Texan serving in the United States Army immediately after the Civil War. Although white males from Reconstruction (formerly Confederate) states were under a blanket suspicion of treason at the time, many non-conformists proved loyalty by fighting for the Union during the War. It's possible that Dobbs was one of these.