I forage or my chickens all the time! But I live in Hawaii, so I can't really suggest what you
should look for during your walks.
Today on my way back from town I stopped to pick up a
bucket of fallen mangos, a bunch of damaged feral bananas, a half bucket of feral papayas, half bucket of guavas, and a bucket of noni leaves and fruits. I got home to find two loaves of slightly moldy bread by my gate that someone dropped off. This all gets added to the various assortment of things harvested from my own homestead and garden. And in the afternoons the hens forage for themselves in their pasture paddocks.
Between foraging, what I grow myself, and what neighbors drop off I buy very, very little commercial feed. Basically they just get commercial feed during a bad weather spell or when I'm away from the farm for a couple days. Plus I put a small amount of scratch in their pens in the evening to entice them back from their pastures so I can close them in for the night in order to have them lay their morning eggs where I can find them.