Next time before you run the break free down the barrel to get it ready for storage.. take a patch and put some isopropyl alcohol on it. As soon as the boiling water is pored though the barrel swab it with the alcohol patch. That will help dry the barrel right NOW. Then feel free to swab the barrel even while hot with the break free. All that will happen is as the barrel cools it will draw that break free into the pores of the barrel. It actually protects it better.

I am going to guess. When you pour the boiling water through the barrel to heat it and dry it, as you set it in a corner to cool, that is when the flash rust is forming. Run the alcohol through it right away and that should help dry the barrel faster. I personally clean my rifles the same way you described, and never encountered that problem you have there.