remember to wear a mask if you are using stall dry. When you stir it the dust has silica in it which is bad for your lungs. You should also make sure all the chickens are out of the coop when you do it.
I use stall dry in my deep litter with shavings. Stall dry is volcanic ash and DE so it should be fine in the compost. I hope so because that's how I plan to use mine. I also go along and sprinkle it where ever there is a gooey poo on a ledge or roost. It makes it much easier to scrape off.