Complex sentence: Since 1938, Maryville High School teams have been using the name Red Rebels, and since the 1960s (around the centennial of the Civil War) the Confederate flag.
Split into simpler sentences: Since 1938, Maryville High School teams have been using the name Red Rebels. Also, from the 1960s the school has used (around the centennial of the Civil War) the Confederate flag.