Jas, for what its worth..."Antique Pistol Collecting" by James Frith
(Arco Publishing;1960) notes that: "From Approximately 1780 to 1800, the duelling pistol was stocked to the muzzle and fitted with a barrel of octogonal section. Sometimes the upper half only was cut to octogonal section, the lower part being round. The barrel was treated with acid to produce what is called a brown surface.This was for two reasons, one to prevent rust, and the second to prevent the glint of metal attracting the attention of the opponent."
pp#26. He didnt foot note his statement.
Then theres a statement in "The Age of Firearms"by Robt Held (Harper and Brothers 1957)on pp#27 that as early as 1440-1470 matchlocks were getting barrels finished with exact octogon flats polished to either mirror finishes or "darkened to eliminate glare by any one of several methods of staining iron by artificial oxidation and acids", which sounds like browning. Again,no foot notes, but both of these authors were researchers and seem to have based much of their books on observations...Held further states (pp#110)that the Brown Bess was introduced with pickle browned barrels (in 1702?)but so were most barrels since the end of the 16th century. They called it "russeting", and an early reference to that is found in "The Gun Makers Rates", a portion of which Held inserts on pp#87 in the same book. This lists the established rate to be charged for many typical gun repairs including "Making clean and new russeting of a musket". These rates were established by a Royal Select Committee in 1631.
Dont know if any of this helps, but it does seem to indicate browning is a very old finishing technique.
TC