The leading publication of browning and blacking formulas for gunmakers is the book "FIREARM BLUEING and BROWNING" copyright 1936 by the author R.H. Angier. You will be able to find this book there in Australia. In addition to formulas, Angier goes to great details of the processes.

On page 80 of his book is a formula for damascus and twist barrels and is listed as B. 12. Under this heading are two formulas and the second one (b.) will be of interest to you as many people use it with success. This formula is added to 100 ml of distilled water

Ferrous sulphate (a salt) 1.6g
Ferrous chloride cryst. 1.1g
Solution of ferric Chloride (29%) 9.0g
Hydrochloric acid D. 1.16 6.5g

Experiment on some old barrels in order to learn how much time you need to allow the formula to rust your barrels, but not cause pitting as the relative humidity effects the process; also to determine how many passes of of the formula application are needed.

In further regard to this formula above, the author states that the Hydrocholoric acid was added to improve the keeping qualities of the formula, which should be noted. You may want to reduce the amount of Hydrocholoric acid somewhat if you see if it is rusting too much during your trials before you actually brown the barrels. One has to be careful with acid. In the barrel blacking formula I use to black the barrels of the double rifles I build, I use a formula (Swiss Black -Beutel) with no acid, using 90% alcohol instead.

Another tip I offer is to use 0000 steel wool to apply the formula to the barrels instead of useing a small piece of cloth or pad of cotton as most craftsmen use.

However the best tip I can give you is to buy Angiers book and read it 2-3 times before you start.

Kindest Regards;
Stephen Howell