@ninnymary yes, I throw everything in the run. Both coop and run are dirt floored, which makes it easier to keep. it is raining right now and I just ran out in the rain to dig out the trench around the coop and run. We are on a slope, just enough to run rainwater into the coop and run. The run is a foot deep in leaf compost, so that keeps them out of the mud. The coop has islands because the girls dig pits, so if the trench is breached, the coop gets wet. I just throw more leaves or pine shavings in there.
I throw in corn shucks, cobs, pea hulls, kitchen scraps, garden leftovers, grass clippings, practically anything. What they don't eat, they scratch to pieces and poo all over it and make me dark, crumbly compost.
Flies? Yes there are flies, but not terrible. MUCH worse with the ducks, glad they are in the freezer. If you rake your coop and run on a regular basis to scoop the poop, then you won't like my method. If you have better things to do than rake poo every day, then you will like the deep litter method. And the chickens love all the interesting scraps and garden stuff.