I deferred for awhile to flytyer's greater experience and fly tying skill. But, being contrary, and being a decent fly tyer myself, I had to test out the Rit on the Schlappen...
I was quite happy with the results. I just used Black Rit, with medium-hot water, left it in for quite awhile--I'll admit I'm not scientific about this--and fixed it with a bit of white vinegar at the end. I obtained a dark, attractive dun. You can get it darker or lighter, obviously, by adjusting the time in the dye bath.
So, while I believe based on fly tyer's suggestion that you could get a nicer color with Fly Dye's Dark Dun, I stand by my earlier opinion. You might be totally satisfied using Rit black.