Monty, are you looking for something you can grow and let the chickens forage in the area, or are you looking for something you could grow in the area, harvest and take to the chickens?
I think it matters somewhat in terms of what to suggest.
Black soldier fly larvae make great food for chickens and convert all kinds of stuff into really good feed (for fish or chickens, probably work for any insectivorous critters, really). But, that doesn't really connect to the question of what to grow in your plot
Some choices are great if the birds are going to harvest for themselves, but might be a pain for a human to have to gather and take to the birds. Some choices are easier for human harvesting.