I disagree with the theory that chickens eat feathers because of something missing in their diet.
Our girls have free access to pellets and spend 8+ hours per day outside slaughtering bugs and worms, eating grasses and seeds, etc. then in the evening get a little cottage cheese, pasta, or other "people food" before bedtime. Their crops are always about to explode by bedtime. There is a wide range of things they won't eat, so they're not hungry enough to eat things they don't like. It's hard for me to believe that they are in any way malnourished, but in any case, they're unable to analyze or understand the composition of things they find on the ground.
Feather eating is normal behavior in many birds. Our hens snap up any feathers they pass and snarf them down instantly. One possible reason may be to recapture proteins needed to build feathers. Another may be to minimize signs to predators that there are chickens in the area. Maybe they just like them.