The problem is the wounds - any time chickens see blood, they will relentlessly pick at the wound until the wounded one is dead if you can't catch it before that. Sounds awful...and it is. But, it's just the way chickens are.
If the wounds are on their backs, you can treat with triple strenght antibiotic ointment - then, I would cover with a chicken saddle to prevent recurrence.
Make sure they have plenty of outdoor access...if they have other things to do (like free range), it'll keep their minds off of pecking each other.
ETA: I feed a layer pellet that I drive an hour to get because it's made with animal protein. Chickens eat bugs, worms, and the like - that's animal protein...they do need it in their diets, and I find my girls have had less health issues with this feed over one such as Purina's Layena, but that's only MY experience.