In a newspaper shown in Ken Burns: The Civil War he is addressed as "Gen. Jefferson Davis": did he ever hold formal military rank in the army of the Confederate States? Did any of his military ranks from his service with the United States (Colonel, Lieutenant, Secretary of War) carry over?
As President, Davis was Commander-in-Chief of the Confederate army. He didn't hold any other specific rank - some United States Presidents did technically retain their previous rank while in office, as pointed out in this other post earlier today, but no President has given himself a military rank while in office.
Davis's previous rank in the United States Army (Colonel) would not have carried over, since no ranks carried over. The Confederacy was a new country, forming an all-new army; the US Army was a totally different foreign service.
(Also, "Secretary of War" isn't a military rank; it's a political office in the Cabinet that isn't involved in the military command structure and can be held by a civilian.)