They fly through the small chicken door? Or you have a large door open for the chickens? You could try hanging a burlap sack over the chicken door. Keep it slightly smaller than the door and push the chickens through it once or twice and they will do it on there own but it would keep small birds...
Are you feeding layer pellets or layer mash? I keep my feeder inside the coop for 2 reasons it keeps the food dry in rain and it keep undesirables from eating it