I know some people successfully brood chicks and ducks together, but I don't. My ducklings have always made a hellatious mess, and my chicks have always been much neater. I brood my ducklings in my hall bathroom tub, and my chicks in Rubbermaid tub brooders.
I also house them separately when they get older, but honestly, I have a pair of year old Pekins temporarily housed with the chickens (while the new and improved duck house is being built) and the mess is not as bad as I thought it would be. It might be because it's only two ducks and 12 chickens in an amply sized coop, or it might be just these two ducks aren't as messy at night as ducks usually are. I don't know.
So while a month ago I would have said I'd never house grown chickens and ducks together, I think in certain circumstances it can work-- you never know.