Nice idea! For bigger work, you can buy silicone rubber brushes in kitchen and BBQ shops. Never thought of using them for soldering.
I've tried cooks brushes before but the bristles for soldering (at least for me) were either too long or too thick. Though they are what I use for spreading wood glue around whilst woodworking (brilliant for this).
Over the years for solder I've used as I mentioned in the video countless small artists brushes that I have ruined, hessian sack, wet rags and stainless steel brushes, but nothing has ever worked as easy as these DIY silicone brushes.
I haven't tried them out for silver brazing/soldering yet, I'm thinking that the silicone wouldn't be able to stand brazing temps?