Whatever veg's you grow in the garden give to them, we do and it cuts back on the cost of other things for us. There are things they won't eat like a radish but they will eat the tops. If you leave a few old cardboard boxes out and wet them, roaches will come and that is a good supply for them, and trust me the chickens will wipe them out clean.
You can also grow wheat, soybeans, berries, grapes, watermelons. start a worm bin (easier than you think), do a herb garden and keep it covered if you want to prosper it, chickens love mint. Or at least mine do.
We all love science here and we a worm bin for the vegtable garden but the chickens like that as well. We just scoup out a bunch now and then and throw them out there. If they survive they survive but seriously with chickens around not likely.
you can also breed meal worms and ugly worms (super worms), they are ugly and crunchy and like potatoe chips so don't feed them much.
For smaller yards there are still easy ways to do this. We have a raised table for the herb garden, (herbs can be grown indoors easily as well, and then you can plae other veggies like lettuce on the table instead, which also makes it easy for us to work off, underneath we store gardening supplies. We raised four beds and in additional to marigolds, which are good to eat in salads and high in vit C they repel a lot of bugs from the veggies, we then place in peppers with our flower beds, pretty to look at and you can store them in white vinger and keep darn well near forever. Chickens will eat them as well and they are good to spread around the coupes because certain predators don't like them.
Other flowers you can grow are panies in the winter time and they are ediable for people and chickens alike. There are tons of flowers that can be eaten that people use in their gardens for visual aspects but work great as food as well.
We also hang tomatoe plants form the patio, cherry tomatoes work the best.
Find a small place in the yard and throw some watermelon seeds, whtey will come up!Lot's of easy ways to grow treats for the babies.