How many birds do you have? Do they have a run? Have they stripped the run of vegetation? I use natural bedding in their coop, with the goal of having a deep composting litter there. That is best accomplished if the coop has a soil floor. This year, is the first year that I have come close to achieving that goal. In the spring, I will clean most of the litter out from under the perches, and toss it into their run. My goal there is to have a minimum of 6" of deep compost. That's difficult to achieve b/c the stuff simply melts into the soil. In the coop, I use a combination of dry leaves and grass clippings, some garden debris, and have the option of adding wood chips (not shavings) though have not added those there yet. The run is all of the above with copious addition of wood chips. 500 s.f. so, that means hauling a lot of mulch material.
I also sheet compost some in the garden, have a hugelkulture mound which eats up all of the compostable material I can throw at it, and have a Back to Eden orchard, and am converting the garden to BTE. All of these take copious amounts of compostable material.
Any composting you do, whether in the run, in your yard with chickens having access to it, or anywhere else will benefit your plantings and your chickens. There really is no wrong way to do it.
