Run a search for "walnut". Should give you some valuable information.
I think I'd prefer the red oak or the ash over the walnut, for a selfbow...but if you get fed up with oak and the ash isn't straight enough, you could certainly try the walnut. Look for STRAIGHT grain, which can be more difficult to find in walnut than in ash/oak. Also, I think that tighter growth rings result in higher density, in walnut. A wide flatbow selfbow should be possible with walnut. Never used it myself, but just some observations from examples on online message boards...