Great advice @MatthewsHomestead! I never thought about the goats and the moisture issue from ducks.
I have sand and river rock under my duck's pool. It is nice as you can hose it down and for the most part the water is contained.
I have been splashed a time or two as well. So know just what...
I put big rocks on top as my muscovies like to perch - might want to consider how to secure it if you use a bucket feeder. Especially with goats and climbing.
I am sure @MatthewsHomestead will be on soon to lend some helpful advice. :)
You could also feed the ducks twice a day as well once they are old enough, you don't have to have food available all day.
That way the goats would be busy eating their own feed while the ducks get to eat. :)
These are some photos with my feeders.
The green one is for the chickens and the bucket feeder for the ducks as I keep my ducks and chickens separated. Well, except if I am out there - I will let them intermingle. I didn't think the ducks could get into the chicken feeder (the way Is is made)...
What kind of feeder are you using? My suggestion - multiple feed stations. Maybe try the no waste bucket or pvc feeders. I have both and the chickens and ducks can use those. Goats shouldn't have access to feed all of the time - so you could use an open feeder for them and feed twice a day...