The Atlanta Southern Confederacy newspaper of May 23, 1861 has the flag presentation ceremony for the Jackson Guards listed.
The flag is described as being: "a most beautiful one, tastefully gotten up and made of fine silk. On one side it has the Harp and Shamrock and on the other the inscription "Our Cause Is Just." The article does not mention the color as being green but that's possible.
The 19th Georgia did not lose their flag at Fredericksburg. The 14th Tennessee, of the same brigade, did. Both flags are ANV Second Bunting issues (with orange borders) and the actual flag for the 19th Georgia is in a museum down in Jakcsonville, FL. The ID of the flag taken by the PA Reserves at Fredericksburg got crossed and the flag has been called the 19th GA ever since, but I have evidence that the 14th TN lost the flag (from a period requisition) and the actual surviving flag of the 19th AG in Florida. Second Bunting flags, when lost, were not replaced with other Second Bunting flags - they were replaced with Third Bunting flags with the more familiar white borders.
I have been working on a book on GA Civil War flags for ten years and have detailed files for some of the 19th GA flags. I have no clue what became of the Co. B flag.
Hope this helps.