I have a compost bucket on the counter that collects all the kitchen waste. Unfortunately, it collects some things that the chickens shouldn't have, like coffee grounds. So the bucket contents go into the compost bin. DH thinks we have too much clutter/junk on the counter already (he's right), so a separate bucket for non-chicken waste is just not going to happen.
That said, I do save some things separate for them, like squash and melon guts, seeds, and rind. That stuff goes into the run when I give them their afternoon snack, which is a mash made out of their normal feed.