Rust bluing is different than heat bluing. To Rust blue, use any browning solution to brown the barrel, then dip the barrel into a trough of boiling water. in the boiling water, the rust color will turn blue. The blue will be as durable as the rust finish is.
Heat bluing requires a barrel length trough filled with coals so you can heat the entire barrel up to temperature at once. Many smiths cover the barrel on all sides with burning coals to reach that critical temperature, and get that even blue color without spots or blemishes. Sometimes the bluing has to be redone, after blemishes are polished, or removed. The trough can be a long channel dug into the ground, if this is a one time deal. Otherwise, you may want to find a machine shop that will weld up the ends of a piece of sheet steel long enough to use for this purpose, and find some kind of steel stand to put it on.
The real problem is working with the heat, to make sure the barrel is being heated the same its entire length, and on all sides of the barrel at one time. Gas burners underneath the steel trough, as you would see in bluing tanks, are probably the easiest way to insure even heating, even if you do use hardwood, or charcoal inside the trough and around the barrel.