J.E. Hewitt was a small boy living in Mansfield at the time of the battle. He interviewed many veterans and researched the battle and I think in 1925 he published his account. It’s widely quoted in writings on the Red River Campaign and generally accepted as an accurate account. It is only a small paper bound book and not in print, very hard to find. They have a copy at the Mansfield State Historic Site.
As far as the flag being the same, the best account is by Col George Soule who stayed with the Crescent through the whole war and was presented to the UCV reunion in 1915. He was discussing the surrender of the Crescent at the end of the war and said, “Its shot and shell-torn banner which received its baptism in the fire and blood of Shiloh’s battle was torn into pieces and divided among the members of the regiment, as souvenirs of a cause in which they had served so well, and of battle and war experiences which were written on memory’s page in unfading letters.” Also, I think we’ve discussed before on this board that there is a piece of that flag at Tulane with a note written by a widow of one of the veterans saying that it was the same flag carried through the entire war. I have collected all I can find on the Crescent’s flag which isn’t much but I’m always looking.