I'm no gunmaker, just a poser working my way through my first one now. But I use flame bluing and linseed oil quench often for little shop made tools (think woodworking chisels, hand plane irons, marking knives, etc.) and such. I think it would be really difficult with a barrel. If I were to attempt to blue a barrel, I believe charcoal bluing would be more HC, and also easier to do in the backyard. A thin gauge sheet steel box could be folded from scrap for free (think refrigerator, washing machine, etc found on the side of the road).
I'm not sure how you would handle the hot barrel, tongs would probably mark it. I wouldn't feel good about shoving a steel mandrill into the bore, .maybe a 3/8" solid brass rod could be used to slide into the bore to pull it out and card it periodically.
Obviously I've thought about this quite a bit for my in-progress build. I think I may just leave it in the white and let it naturally rust and patina as I clean it off, but it's still something I'm debating