A tiny account of our daily happenings with our little flock of backyard chickens.
When we had birds (though we had hundreds more than you have) we would keep a waste container under the sink. Any food type waste went into it and would get fed to the chickens. They eat everything. Eggshells (good calcium boost), melon rinds, fruit and veggie peels, etc. Essentially the same stuff you'd put into a compost pile you can feed to the ladies first.
We have a compost bucket in the kitchen and have been tossing it into the compost heap. Now we see we can feed (at least some of) it to the hens. Hooray!