There was a good thread with pictures here on BYH recently, but now I cant find it! Ill try to describe what I remember...
Using a round, top filler feeder, you just take a piece of no-climb fencing with small openings, and wrap it all the way around the sides and top of the feeder. You need to be able to secure the feeder so it cant be tipped over.
Using a long, tough style feeder, you put it up agaisnt a wall, then secure the same kind of fencing so it kinda leans from the ground to the wall, shielding the feeder. Be sure your feeder is close enough to the fencing that your chickens can reach the food through the holes. It'll be easy to adjust, just watch your goats for a moment and youll see them trying to get the food, then youll know how close to put the feeder.
The fencing holes should be small enough the goats cant get their noses or tongues into the feeder, but the chickens can get their heads through them. I *think* the fence hole size is 2X4 inches, but maybe its one size down. My Jersey Giant hens can get their heads through that size fencing, but my pygmy and nigerian dwarf goats cant.