There are many ways to do this. First you need to decide what look you want your wood to have. For example, if you want your wood to look like the finish on old figured Winchester wood, you will need to apply two different stains. First is a wiping stain which will make the figure come out. An example is one that .38 cal mentions called Herter's French Red. A wiping stain has a pigmented filler in it that will make the figure come out and fill the pores about 80%. It used to be sold by the old Herter's company (guide proven and world tested) and is still being duplicated and sold through Brownell's. I have not tried the new stuff as I still have supply of the original but it was (is) probably made by the same company and just repackaged and yes it does take the life out of checkering tools a little faster. I usually need a new cutter for every panel but they are cheap. Once it is dry, then you can add a very dilute mix of a water stain to give it that warm golden look. Brownell's sells some excellent water stains that you can mix to suit your needs. The two most common ones that I use are a combination of Resorcin Brown and Orange II concentrate. Minwax also makes wiping stains that I use occasionally but they don't have the silica filler. After you've achieved your desired color, then you need to apply the proper finish. For this type of coloring, you almost exclusively have to use a finish that builds up and forms a top coating such as Birchwood Casey's Tru-Oil. This will make the grain jump out and change figure as you move the stock. Keep in mind that wiping stains will give the wood a muddied look but most old American high grade guns were finished in this fashion. Also, wiping stains don't penetrate the wood very deeply and you have to be very careful so that you don't sand through it as you build your finish. In my estimation, this is the best way to finish American walnut and have it look old.
You can use water stains exclusively and I dilute them quite a bit so that I can control how much goes on and where it goes to get the desired look. It may raise the grain again in areas so you will have to resand some spots but this is an easy method to control. Water stains will penetrate the wood more than wiping stains
Another way to go at it is to use the newer NGR's or non grain raising dyes. These penetrate the wood more deeply and you have to be very careful as a little goes a long ways. I will dilute mine with alcohol or Behlen's Solar-lux reducer so that I can apply several light coats to get the effect I want. Behlen's and Laurel Mountain Forge are a couple that come to mind. I don't use them very often, because they don't produce the colors that I am looking for. Each piece of wood is unique to itself and you may have to try several to achieve what you are looking for. I probably have 10-15 bottles of water stains mixed in various ways and numerous cans of wiping stains along with a half dozen or so NGR's and I'll do something different every time. To me, a good figured piece of American walnut must be stained to bring out all its glory or it will take on a dead look.
If your working with the English walnut, then stick with a water stain or NGR to even it out or give it a littler reddish look if you desire. English walnut should be finished with a penetrating finish that doesn't build up on the wood. Some good ones are produced by LMF, Pro Custom Oil and Dembart. LMF calls theirs Permalyn. You can actually get by with just the sealer for a finish. The regular finish dries too fast in my estimation and is harder to work with. I add about 15% boiled linseed oil to it to slow down drying time. If you desire to mix a little oil in your finish, make sure that the oil you are using is compatabile with the finish. That is linseed oil to a linseed based finish and tung oil to a tung based finish. Also, a lot of finishes now days, advertised as tung oil do not have much actual tung oil in them. While using these finishes on English walnut gives the desired look, I still have water spotting when it rains.

Hope this helps and I'm sure there are lots of other good ways to do this besides what I have written here. Bob
As a P.S. I just remembered another stain that I really liked when working on my last muzzleloader and it's called TransTint. Spendy and lots of different colors to buy but worked well on maple along with some other water stain.