We have two Nigerian Dwarf goats that live with our 24 hens very nicely. First goats should not eat chicken feed, it is like crack to them and they will bloat if they get to much. I would say that this is the biggest challenge to keeping goats with chickens. So just make sure that they cannot get to the chickens feed. We accomplished this by making the doors on the chicken coop as small as possible and placing them high enough off the ground so that the goats could not jump in. The chickens fly in just fine. I thought it important that the goats had their own house and that the chickens not be in it pooping in their hay and/or nesting in it. We hung a heavy rubber mat over the door and the goats just push through, but the chickens have not even attempted to see what is on the other side. Mini goats are pretty inexpensive ours have about 10,000 sq ft of pasture/browse and we only went through about 5 bales of hay in 9 months or so.
Chickens will happily eat goat poop. Which is nice because they keep the pasture clean. As long as the goats are healthy this is really not a problem. Our hens look great and lay very well. Maybe they get extra nutrients? Any way, good luck and best wishes.
As far as housing with ducks, just make sure the goats have fresh clean water. They can be a little picky about dirty water, and ducks love to make water dirty!
Any way, good luck and best wishes. It can be done, with a little ingenuity and persistence.