Chicks and ducklings are best kept separated. Ducks love splashing water everywhere. Chicks don't care to be wet and may get chilled. Ducklings also grow much faster than chicks.
Yes, ducklings are very messy in the brooder and most folks will keep them separate from chicks, which have different needs. The chicks need to stay dry and are much safer with a shallow container of water to avoid accidental drowning, and they also happen to be very susceptible to illnesses if they become wet. The ducklings need a source of deeper water so they can wash their nares and eyes. Usually chickens and ducks will get along fine as adults. Hopefully you won't end up with drakes that may possibly try to mate with the chickens, as that could be harmful to the hen.