Weeds are all well, good, and useful, but it would be hard to harvest a lot of seeds from scattered crops of weeds, unless the chickens are free-ranging *for themselves. I'd rather invest in seed packets of quick-producing stuff, like sugar beets and kale.
Because they can't live off that indefinitely, and remain healthy. Chickens diets in the wild are mostly insect and seed, which I don't think is sustainable, in the situation you describe. If you can get oats, or other kinds of grain, to feed mealworms and such, why aren't you already feeding...
No free range at all? I'd be getting rid of the chickens and keeping geese. For them, I can cut weeds through most of the year, and supplement with some squash and old lettuce. I wouldn't get many eggs, but I wouldn't be getting them from the chickens either, and I'd be able to raise a pretty...