I've taken these types of statements to be symbolic. I cannot see a soldier saying, "We followed a different flag before this flag, and then we followed yet another when this flag was replaced."
I'm going through this with the 12th Mass. Infantry national flag, were the Stoughton Sentinel, May 9, 1903 reported, "Gentlemen of the Board of Selectmen: we have come here tonight the only four surviving members of the Co. that went from this town 42 years ago to-day and on that anniversary we wish to present to you the flag which was given to us in Morton's square by Sylvanus C. Phinney; we carried that flag through three long years of war it was used to cover the bodies of all the soldier dead who were brought home from the front and since the war it has been in my possession and we are getting old and soon will pass away." The Massachusetts State House collection has another two 12th Mass. Infantry national flags.
Ed