There are many reasons chickens eat each other's feathers. Some reasons are stress, poor nutrition, and boredom. Stress can be health stress (worms, lice, mites, disease, heat, cold), it can be social stress (aggressive coop mates, over crowding, unruly neighbors), and it can be fright (predators near the coop, predators sounding in the distance, predators flying overhead, new surroundings).
Here is a summary of things you can try to stop feather picking
Good nutrition and a healthy environment are important for all chickens. Feed a good layer ration, always provide crushed oyster shell, keep the water clean, and provide green leafy vegetables. The vegetables and oyster shell provide calcium. The leafy vegetables also entertain the flock. Scratch grains, in moderation and with grit, are good.
Stress can be health stress (worms, lice, mites, disease, heat, cold), it can be social stress (aggressive coop mates, over crowding, unruly neighbors), and it can be fright (predators near the coop, predators sounding in the distance, predators flying overhead, new surroundings). To avoid stress make sure the coops are large enough and provide good shelter from wind, sun, and rain. Coops near aggressive neighbor birds are stressful. Heat, cold, introducing new birds, and other changes in the environment are also stressful. Make sure the flock is healthy.
Provide a variety of toys and treats to prevent boredom and to exercise the chickens' natural desire to peck. Give them scratch grains, day old bread, cabbage, cauliflower, kale, or watermelon slices (especially the rinds). Plastic food containers with the lids make good drums for the birds. We hang a mesh bag on a string and the flock plays tether lettuce. Keep changing what you provide; they tire of the same old routine.
Sometimes picking begins when nests are very busy and well lighted. Birds pick the vent of another bird as she lays her egg. Place nest boxes away from the flock's favorite stomping grounds. It also helps to place the nest boxes in a dark area or cover the entrance to the nest box with a cloth.