Chickens are not compatible with a growing garden IMO. However... that being said, I got chickens for the express purpose of helping me with my garden. And I consider their contributions to my gardens to more than compensate for the many anti tank traps they have created in my yard! The way I manage them: my garden(s) are fenced during the growing season. As soon as the crops are harvested, I take down the deer netting. The flock has access (during their free range time, which is limited due to hawk predation) to the garden from mid/late Oct. through early April. They turn the soil, eat bugs and weed seeds, eat any remaining vegetation. They actually seem to enjoy eating rhubarb leaves, in spite of all the other greenery available to them. Then, the deer netting goes back up. Year round, their coop and their run are managed with deep litter. My ground is frozen from Nov. through mid April. But, even then, the girls stay busy making compost. I build them a 4' pile of garden debris in their winter run/sun room. In addition to that pile, there are bales of hay, and a section covered with 2' of leaves. Any time the outdoor temp is above 15*, the girls are lounging in the sun room - digging in the leaves, dust bathing, finding all sorts of goodies to munch on. In the spring, I can haul many loads of black gold from their sun room to the garden.
Some people are able to allow their birds into their growing gardens for short periods of time. Others fence individual beds and let the birds roam the paths. Some folks divide their garden in half, and have their coop in the middle. Garden and run alternate from one side of the coop to the other. Still others build tractors that fit over individual beds. These tractors can be moved from bed to bed as crop harvest/planting dictates. I'd love to be this neat in my gardening approach. Not gonna happen, thus my name!