Do you know of anyone that uses one of those that actually works? We had one and it didn't work for rabbits much less birds.
Could you cut strips of plastic like 1" wide to hang over the chicken door either inside or outside of it so the door going up and down isn't affected? The chickens should get used to it but the birds won't.
If there are places they roost that chickens can't get to, make nail spike boards to nail to those places so they can't roost in there.
Keep any chicken feed sealed up other than their feeder.
Good luck!!