The battle depicted is Antietam (Sharpsburg) in Maryland in 1862. Some of the Confederate units are shown carrying blue and white "Hardee" style battle flags, which were only carried in the Western Theater (Tennessee, Kentucky, Georgia), not at Antietam.
McCoy's Sgt stripes are sewn on patches, instead of stripes individually sewn onto the sleeves, which was the norm for Confederate enlisted rank.
In the battle of Antietam in 1862, Kirk is shown using an M1863 Springfield rifle-musket, which model was not yet developed at the time of Antietam.
The US flags show 36 stars for 36 states, but in 1862 at the time of the Battle of Antietam, there were only 34 states and so should be 34 stars. The 35th was added in 1863 and the 36th was added in 1864.