Oh joy! Lots of terrific compost there!
Okay. Now I'm going to be very serious. Don't even stir that mess up without wearing a very well fitted dust mask. Hanta virus, aspergilliosis, and plenty of lung destroying dust are real risks. Chickens have even more sensitive respiratory systems, so it goes without saying that it needs to be shoveled and cleaned out. But please do not expose your chickens to the premises without doing some smart things first.
I just got through posting on another thread where someone had just bought a farm and was facing something similar, but with the addition of a live flock of semi feral chickens that had never been properly cared for. I recommended feces samples be sent to a lab to identify the presence of Marek's or other contagious diseases that linger active in the soil and premises sometimes for very long periods and can be passed on to a new flock inhabiting the site. I urged this should be done before introducing any new chickens.
The reason I urge this is because my flock was infected with an avian leukemia virus somewhere along the way, perhaps even in the very beginning when I adopted two adult hens from a friend that had a coop that looked exactly like the photos you've posted. Now the disease is in my flock and I can't get rid of it.
Before you invite the same kind of heartache I've experienced, please take the time and spend a nominal amount of $$ and collect some feces and soil samples and send them to a lab for a quick test so you will know what you're dealing with.