It's most likely from having the ducks in with them. As you noticed the ducks stay wet and keep the brooder floor wet and make a royal wet mess of the water. The chick's little belly fuzz gets wet and falls out from being rubbed against the brooder floor. They'll be o.k. now that the ducks are out of the brooder.
I learned the hard way, just recently, not to put ducklings in with chicks. I've done so in the past with no problem but had a batch in a Chick-N-Hutch in the coop with two heat lamps, raised wire floor and somehow during the night the power strip defaulted and the lamps went out and of course, the temps dropped also. The next morning I had several dead or dying chicks all laying around the brooder floor completely SOAKING WET - looked as if they had been drowned. I know it was the ducklings that got them so wet. If the ducklings had not been in the brooder, the chicks would have huddled together and stayed warm enough and dry enough to survive the temp drop and light outage. Ducks are wet and messy and should not be in with baby chicks. I'm posting my experience so others will learn.