When you say small coop, how big are you talking? I don't think 15 chickens would fit in what I'd consider a small coop, let alone any ducks.
given enough space, especially in the run, chickens and ducks can live together. I would not brood them together, though. Ducklings are about the messiest creatures on earth. They love the wet and the damp and make huge messes. Damp will kill baby chicks faster than about anything, so the two don't mix very well. Once the chickens are older and have decent immunities, plus lots of space to have a dry area, you'd be fine to combine them.
I kept 4 ducks in my main flock for a few years. Feed was in the coop, water was in the run. I used a kiddie pool for the ducks to drink and bathe and they did fine. All the water stayed outside, and the coop and run are both large and the chickens had lots of dry space.
you will want to keep an eye on your chicken hens and drake ducks, though. Drakes are one of the more sexually aggressive animals and can injure chicken hens. Mine were older and had bonded to their duck hens when I added them. Plus, as I keep harping on, everyone had lots and lots of space to get away from each other. I'm just concerned you don't have enough room.