The 27th Miss. did indeed carry an Augusta Depot flag from February, 1864 onwards. As part of Hood's Corps it might even have had the unit designation in cut and sewn white cotton with "27th" in the upper quadrant and "Mississippi" in the lower.
Prior to this time in Florida the predominant flag was the First National so that was probably what they had. I know the 9th Mississippi also staioned there had one.
After this they may have had a Bragg pattern battle flag based on their corps assignments. Some of the other units of those corps carried those. This might have been one of the rectangular patterns rather than the square versions. For 1863 it gets very dicey as it does with a lot of other CS units with all of the altering of brigades, divisions and corps. This could be anything pretty much or they still used what they had in 1862.
We know a lot about AOT flags during the war but there is still a lot we do not know as well.
Greg Biggs