Amaranths would grow beautifully in your climate, the chickens love the seeds. Sunflowers are another favorite.
If you have a chicken run I'd suggest growing a fruiting vine over top. Shade plus food!
I sprout lots of grains for my chickens, wheat and rye are their favourite. I've also used a seed mix called "forage mix" that I grew in succession for constant food supply.
Do you have a compost bin?
A lot of these are weeds, and I didn't plant them myself! My nine chickens live on a very small suburban lot, and I rotate them through four or five different sections, usually moving them once a week. They eat more than just the above, including some of my ornamentals (for instance, they seem to really like rose leaves), bugs, and I also provide chicken feed.
The chard and brassicas come from seed I save myself, and I keep it in a jar labeled "chicken mix" along with winter rye, crimson clover, and some other random seeds. The rye, crimson clover, and alfalfa I bought in bulk as green manure. Any sort of pasture seed mix, or cover crop mix would be fine to grow on as chicken forage, and mixed seed will be better than just one variety of seed.
Bear in mind you'll probably have to grow the forage for several months or even up to a year before you can let chickens onto it; they will destroy it if it's not well established--ask me how I know
There are few things chickens will not eat, and there are many things they will thrive on that many don't think of. They love any kind of meat or dead animals....either cooked up (I use my solaroven, so the energy is "free"), or simply allowed to ripen and become maggoty. Black soldier flies are easy to raise and they can eat the chickens' own manure (as well as every other kind of manure including your own!) and all manner of other vile stuff, and turn it into feed. I feed my layers on leached, boiled acorns.... If you are near a town, the dumpsters can likely feed them too......