You can use the same rust process described in the 'Cold barrel reblueing' - just omit the boiling water step. Rust finishing is a very rewarding process (if you've got the time and patience) as it is controllable for beginners and if you are not happy with the result, just De-Ox it back to white and try again.
You will probably find that the damascus pattern will 'take' with a degree of colour variation, which may vary along the barrel as well within the 'coils'. If you want an even colour, you may need to take it to a deep plum brown - personally, I quite like a honey gold and feel that the variation in colour is perfectly acceptable.