You can buy alkanet oil as part of a refinishing kit like Purdey's Warthog Finish (why warthogs were ever associated with gun stock finishes escapes me, but never mind: the kit does perform as advertised). This is probably the best route if you only plan to refinish one gun. Or, you can make your own in whatever amount you want, as it keeps indefinitely in a sealed container.
Alkanet root powder
Boiled linseed oil (artist's quality, if you can find it)
When I bought my bag of alkanet root flakes from a herbal supply company ten or so years ago, it was only offered in flakes or roots, not in powder. If that's all you can find, grind the flakes to powder in a small mill like a mill for coffee beans (you can get rid of most of the reddish stain by then grinding sugar or coarse salt in the mill).
Then add alkanet powder to the boiled linseed oil in the ratio of 1 Tablespoon of alkanet root powder to 1/4 Cup of linseed oil. Shake or stir daily for a few days. Heat will speed up the process, but stay away from direct heat, or you may torch your kitchen ceiling. If it's hot enough to make sun tea, it's hot enough to make alkanet oil. Finally, strain if needed. Store in a tightly covered container.
Alkanet oil gives a reddish tone to walnut. I use a coat or two, well rubbed in by hand, after coloring the stock with aniline dyes but before any sealer or finish coats. It is additive, so more coats will slightly darken the wood. (You could, of course, simply do an oil finish with the alkanet oil.) After the finish is complete, I typically add a well rubbed in coat of alkanet oil and repeat periodically.