I've never used it on an Arkansas oil stone. The last time I used an Arkansas stone was back in the early 70's, at which point I switched to the RazorEdge silicon carbide stones used dry for the next few years. After that I went to Japanese water stones. My flattening stone is quite rough, almost like a bubbled pumice stone texture but harder. I've seen similar looking stones being sold as cooking grill scrapers, but I don't know if those were made of the same material.
But living in Japan for almost 20 years, and watching the Master Sharpeners at work, and seeing the dished stones that they worked with, I've pretty much stopped worrying about flattening my stones all the time. When they get about 1/4" down in the center I begin to think about flattening. That's about what I would see them using on a daily basis. They would sharpen on a short section of the stone, wearing it down first in the middle, then on the ends, then finally flattening it when it started to look like a dragon's back! None that I ever saw were really concerned about having an absolutely flat stone.
EDIT: Here's a snapshot I took of one of the professional sharpeners working outdoors in my neighborhood in Japan... Note the condition of his stone.
Stitchawl