I'd put them together. I've raised chickens with ducks, geese, turkeys and guineas without issue. One of the biggest problems with waterfowl is they are messy, and they tend to thoroughly wet things down in the brooder, which isn't good for the chicks. So, you need to keep things as dry as possible for the chickens. I put my drinker on top of a Tupperware bowl with a hardware clothe lid. When the ducks would play in the water, most of it would go into the bowl and I could just dump it everyday and remove any wet shavings from around the edges.
And yes, the ducks can't do medicated starter. They should be fed a high protein game bird or waterfowl crumble. The issue with the medicated feed is that the medication blocks the intake of essential nutrients and vitamins (thiamine, mostly) which starves the cocci protozoa and keeps them from overloading the bird. Thiamine and niacin are very important to waterfowl. Without them, they can develop some serious neurological (thiamine deficiency) and leg issues (niacin deficiency). The ducks will also require a higher protein feed because they grow much faster than the chickens, aim for about 20-22% protein, the chicks will be fine eating their food though. I feed my ornamental chicken breeds game bird feed, and they do so much better on it than layer pellets or a lower protein all flock formula.
I hope this helps you out a little, best of luck!