Personally, I think a double doorway is always useful. Basically just a frame and walls/fencing making a secondary entrance like you'd have in an aviary, just big enough so you can fit inside it while both doors are closed. That way, you'd have absolutely no chance for anyone to get in or out if you don't want them to. If a bird would get out past you while you're entering, they'd just go right into the already closed secondary entrance, and if one of the dogs would get in while you're walking in, they'd only get inside that secondary entrance and you could get them out before closing and opening the sliding door.
You could also make it a little wider and use it as a small storage space for feed and such.
As for the chicken door, are you connecting it to a run? You could get one of those doggie doors with a flap, I think it'd look quite nice and it keeps warmth in. Personally, I use an old repurposed window as a door for my ducks, and I'll be installing some vinyl to keep the wind out when the coop door is open.