I think that with the foraging of chickens there is a strong tendency to over-estimate the "carrying capacity" of a suburban yard. In Southeast Asian, home of the chicken, it isn't uncommon to see the village flock 1/4 mile and sometimes much further from home. They aren't out for a walk; those chickens are looking for food.
From ranging over nearly a square mile, to living inside a residential yard -- within just a few days, even a small flock has found and eaten all the easily available food. Then, the
destruction begins.
Now, having said that, around here it is completely reasonable to expect to harvest 2 1/2 tons of hay from an acre of land thru the growing season. That would be over 1,000 pounds of alfalfa or grass from a 1/4 acre. Or, one can grow 500 pounds of grain per 1/4 acre.
Farmers can put their livestock on forage turnips and expect that they will have 3 or 4 tons of dry matter forage per acre from that quick growing annual. The livestock isn't on that land from sunup to sundown, everyday. The crop has a chance to grow, unmolested. The problems with the birds eating immature plants, scratching and fouling their pasture with too much manure, is limited.
Probably, the most appropriate crop to grow in a suburban yard is lawn grass, in my opinion. My chickens prefer Kentucky bluegrass to just about anything else out there. They won't do a good job at
mowing and really tend to pile poop inappropriately. This year, I decided to move them around the yard in what I call their "playpen."
Sand Hill Preservation sells seed mixes of
"Chicken Treats" (click). These are mixes of annuals. Other than that, you might think about appropriate pasture or lawn mixes available at farm supply stores and garden centers.
Steve