It’s best to store textiles flat or rolled. I like to use a couple of tubes, rolled cardboard or paper to store longer pieces of cloth, hangings or scarves. The two tube trick controls the fabric neatly without adding creases folds or bumps from fringes. The diagram shows how to roll one or more pieces together, stack multiple pieces all on tube 1, then roll as usual.
You can use card inners from packs of tin foil, or make rolls paper. I cover mine with acid free paper.
It is worth including a printed copy of the instructions when sending work out, so that the recipient can store it safely too. Feel free to download and print.