I have used flux brushes too, as has probably everyone else at one time or another. I usually cut the bristles to half their length which made for a little stiffer brush and I also would crimp the ferrule with a pair of flat jawed pliers just above the bristles to get a firmer grip on the bristles so they wouldn't fall out and end up in the glue.
I use the Rockler silicone brushes and I don't let the glue dry, I drop it in a small container of water and wash them out as soon as I can aver use. I do that because I didn't want to be pulling a glob of glue and bristles off after it dried even though they claim you can do that. Yes you can but it weakens the bristles a little each time I'll bet. Pretty soon you need to buy another one.