It is my experience that the further away from Washington City the Union Army was the less likely any flags they captured would be turned into the War Department.
All of the Northern state collections that came into being after the war (and some still exist) came from flags that were not properly sent into the WD.
Grant's report for Vicksburg claimed 85 flags; none were sent to Washington. Rosecrans claimed 18 (maybe 16) flags at Corinth - none were sent to Washington. None of the many flags taken at Ft. Donelson were sent in. By contrast, most of the Mill Springs captures were sent in along with most of those from Missionary Ridge, Atlanta Campaign, Franklin/Nashville and Stones River.
I do not recall any of the flags from the 1865 NC surrender being sent in - but I will double check the list to be sure.