Chickens will eat and scratch up anything you try to plant in the run that they can get to. What you are left with is dirt. They do fine on dirt. They really like to dust bathe in it and scratch around in it. They can find grit in dirt. My run is dirt.
I personally don't like any organic material as a cover in the run, things like wood chips, wood shavings, straw, bark, or anything else that could be used as mulch. Mulch is used to hold in moisture. Some people do and like it, but I like a dry run. I consider a wet run more likely to harbor disease, or if the stuff gets wet it might get moldy and they can get sick or die if they eat mold.
We all have different conditions and circumstances. You may be able to keep bark or something else in there in the run and keep it dry. Maybe you'll change it out if it gets wet. I don't know how you'll manage it. And just because something can harbor disease or mold does not mean it will. As I said, you can find people that use stuff like that and like it.
To me, the main criteria in maintaining a run is to keep it dry. Rain water should not run into it and it should drain when it gets wet. If you need to add something to it to help keep it dry or to drain, I suggest adding sand. Sand drains really well. They love scratching and dust bathing in it. Some people with small runs scoop the poop out of it, much like a cat litter box to help keep the poop build-up down, or they just rake it. The chickens can even eat the sand for grit. If you have to add something I'd suggest you consider sand.
