From observing my girls on the range they would choose sorrel and fresh young grass tips in the spring, and mature grass seed heads in the autumn. My garden was quite wild but I didn't notice to what extent they chose or didn't choose things like clover, toadflax etc. In the veg patch they would try to eat anything that was young, tender and succulent, so the leaves on beans and beetroot, and lettuce! Many chicken are keen on soft fruit, but its not terribly good for them. My lot were not interested in cabbage leaves or similar, but I know many hens are. I'm sure I have seen pictures of hens eating pumpkin/squash. Possibly something like a courgette might work as well.
Given calendula (marigold) is used in some feeds to give good colour yolks, I might try a packet of seed and see if they eat the flowers.