By Union flag, I presume you are referring to a Regimental National Colors ( State Colors) & Regimental Colors, if so these are battle flags, which according to U. S. military tradition are attached to the staff by a method to avoid or impede capture. Rolling (furl) the colors around the staff and using a cover was the normal method of storage. Cord and tassel was used to tie the furled colors, if, available.
Confederate & Union regiments furled their battle colors on the march or camp, unfurled them when forming a line for battle. I don’t have Hardee’s Drill Manual at hand but I think there is a section on this regarding the Color Guard.
Happy Trails!
Tom Martin
www.Confederate-flags.org