If you turn that run into a deep litter, that will help immensely. As PP stated, your coop and run space are both on the tight side.
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I wouldn't put vaseline on them. Instead, I'd look into finding the root of the problem and fixing that. Start by enlarging your run, giving them multiple levels of roost space, hiding places, and maybe multiple feeding and watering stations. Make sure they're getting plenty of protein. If you can, let them out to free range now and again. Maybe try a flock block for them.About that vaseline thing though, I read that it can be bad for the chickens if they eat it so is it okay to put it on their feathers that they are pecking?
No...the birds need to eat some animal protein...mealworms, scrambled eggs, meat scraps, freshly trapped mouse, etc.Animal protein for their feathers