Rubbing down a barrel with a roll of canvas between applications of solution removes the loose scale and red dust off the surface of the barrel. You will still end up with a matt finished barrel of that's all you do.
Carding ALL of the scale off with 0000 steel wool right down to the steel will yield a barrel that will have whatever polish you gave it prior to browning, like those shotgun barrels. If you want a brown like those shotgun barrels, you must polish the barrel to a mirror finish, may I suggest 1200 or even finer. You must remove ALL of the scratches left by the previous abrasive before going to the next finer one. Otherwise, you will have scratches in the steel that will show up badly and you'll be disappointed with the finish. You will find too that as you go to finer and finer abrasives, it takes less and less time to remove the previous scratches. In other words, you'll spend way more time and effort removing the drawfiled scratches, then the 120 grit scratches, then the 180 grit, und so wieder.
An application of linseed oil or varnish will not disguise the scratches left behind...no matter how glossy.