I think this drawing is incorrect. The 20th Mississippi was part of John Floyd's Brigade and they arrived after their time in Virginia at Bowling Green, KY in very early January 1862. Once there, they became part of the Army of Central Kentucky.
Later that month that army adopted a distinctive battle flag designed by Gen. Simon Bolivar Buckner. When his division, including the 20th Mississippi, were transferred in February 1862 to Fort Donelson, they took these flags with them where some were later captured.
The first of the Hardee flags, based on those that survive, were blue with a white hoist edge only. There was no other white borders for these flags. In the center, again based on surviving flags and written descriptions, had the unit designations painted in the center of the white circle. That is what the 20th Mississippi's flag would have looked like.
What they carried in the Vicksburg Campaign in 1863 is problematical and not many clues survive. In 1864, however, as part of Leonidas Polk's Army of Mississippi, they would have received the 12 star battle flag of the Mobile Depot.
Greg Biggs