A couple possibilities come to mind...mind you, I haven't tried any of these yet, my flashes are still wandering around loose.

Storage – Loop the flashes as they’d be when you normally wear them and…
1. Hang them on a rotating tie rack.
2. Display them on a peg board in the closet.

Packing – unloop the flashes and fold the elastic over.
1. Place the flashes in the pockets of the shirts you pack (providing they’ll lay flat).
2. Use that old underwear you never wear anymore and fold it into a square with the flashes inside. When you put this into the suitcase, place it between shirts that lay flat or, if you must, in the folds of trouser legs.
3. Put some Velcro in a file folder and fasten the flashes in there and pack with your computer.