Mine strangely love Bermuda grass, which is supposed to be high in calcium and other nutrients. When they have access to the yard with the Bermuda grass I notice that their eggshells are thicker. During the height of summer when there is a lot to choose from, it's not their first choice, but they're especially happy to have it when other greens are waning.
They love a good pumpkin, so I try to get extra leftover ones after Halloween. I also grow some for them.
Kitchen scraps are great. My neighbors send over theirs as well.
My girls just look at me funny if I give them amaranth. They won't touch it. Maybe they're just weirdos.
Think long- term, trees and perennial as well.
Siberian pea shrub is supposed to be excellent chicken feed. I think I killed mine though, haha. Need to get some established. Bonus is that it fixes nitrogen.
Mulberry leaves are also supposed to be good. I planted a black mulberry near my coop last year but it will be a while before it's big enough to provide food.
I also planted some grapes for them which aren't particularly nutritious but make nice treats.
I got Hopi purple corn from Baker Creek. It's supposed to be high in protein. I got it for me, but if I can get it to grow well I could give some to the girls. I only got a couple of small ears last year, but we have challenging growing conditions. This one also looks like it might be good for chickens: https://www.rareseeds.com/corn-atomic-orange
My girls "free range" in most of an average small town back yard (fenced to keep my little Hobbits from going adventuring with Gandalf). There are lots of good hiding places, including oak scrub and a giant prickly pear that they have now decided to lay under, lol. Does not make getting eggs easy. The compost pile is in their yard and they like to pick through it when I bring out a new bucket. I let weeds and wildflowers grow, and encourage choice weeds. When monsoon comes the girls have a nice big summer buffet and require a lot less food from me. I put chicken wire around new plants I try to establish within their area. I started letting them out there a few months after planting a nanking cherry that has never been protected from them. They like snacking on its lower leaves but have surprisingly not killed it and it's doing great. They haven't messed with an unprotected pecan sapling, either. The mulberry and persimmons definitely needed to be protected, though. They occasionally snack on my rosemary but have done it no harm; it was well established already.
Do some research before feeding acorns. I've read they can be toxic, but there are people on both sides of that camp. I've decided to err on the side of caution and not feed them directly, but it's not like I go pick up every acorn either!