I have not tried this, but, I have had the loose end of the fly line (while stored on the spool) "work" its way under a wrap or two and then cause problems when you use the spool. If your fly lines have a loop on the end, you could pick up some of the wide rubber bands and loop-to-loop them onto the end of the fly line and then stretch the rubber band around the spool. This would keep the end of the fly line from "working" under a wrap or two of the fly line plus keep the rest of the fly line from coming off while stored.
Fly fishing and fly tying are two things that I do, and when I am doing them, they are the only 2 things I think about. They clear my mind.