I am also concerned about chicken wire on the floor - especially if it covers the floor of the run. If it does, I personally would go to the trouble of cutting the wire around the edges of the run and removing it. If it is just chicken wire, it won't necessarily be hard to do, it will just be time consuming - and may give you a back ache from bending over for so long! Having wire on the ground will prevent your chickens from doing what chickens love to do! I think they instinctively scratch and hunt and peck for whatever treasures they can find all day long. Wire covering the ground would make that painful, and likely impossible, for them to do. Not to mention taking away their pleasure of dust bathing and digging a hole in the cool earth to take a nap when it is hot outside. I think it would be hard to put down dirt, sand, or whatever, deep enough that it would allow them to do all that without the wire interfering. Even if you were able to get it deep enough initially, you’re going to lose so much as time goes on.
As far as what to use to cover the ground, we put down a layer of sand and then a layer of wood chips. It always looks clean and never smells. When it rains, the water seeps down through the wood chips and they dry very quickly once the rain stops. We have found it to be the perfect answer, although of course others have their preferred methods as well. Whatever ground cover you choose, please think about removing the chicken wire. I know you love your chickens and just want them to have a happy life!