After a brief research, it appears the flag at the OSHM is probably that one as it is attributed to the 7th. THe one the author mentions he says there must be a mistake as that in the office of Fletcher is attributed to the 7th. That is why he is asking for someone who was at the surrender to verify it. The letter was written after the return of surrendered flags to the State and it may be that Fletcher, being prominent, was allowed to display it in his office. It belonged to the state and evidently later went back to the state when they had somewhere to store them.

Research shows the 6th Ark flag was retired late in 62. They were consolidated right before Stones River with the 7th so the consolidated flag at the OSHM may very well be the one mentioned in the letter. The author probably forgot about the retiring of the 6th's flag prior to Murfreesboros. One other confusing thing, on Gibson's CSR it states he transfered to the 26th Alabama. He must have came back at a later time to have witnessed the events he speaks of.