To me, "burnish" means to rub with a hard smooth object, polishing the metal (or wood, which can be done with a horn, bone, or steel burnisher) without removing any metal. Pressing it flat and smooth and shiny. Although in modern advertising parlance, "burnished brass" means basically the opposite. A dark fake patina.
Easiest and best way to "age" brass is just to handle it. Dirt, grime, sweat, and blackpowder funk will turn brass a mellow, darker color on its own. To make brass REALLY look like 200+ year old brass takes tricks that I don't know. I can make brass dark, but it still doesn't look like the old, brown brass I see on old guns.