I have the exact same quantities and breeds, I have not found a way to keep them away from the food yet, but I am not trying.
ETA: I mix my own feed so I try to have it so that goats can eat it as well, but they really don't like the chicken food only the baby tastes EVERYTHING!
Our chickens are in a shed with a regular human door that we shut whenever the goats are out. The chicken pen has a gate that also stays shut and we keep the food inside the chicken house in big barrels.
Be careful - if your goats ate enough of the chicken food they might get sick. You may want to drench them with baking soda just in case. Search this forum for that to see what else is recommended.
I just hung the feeder up higher and put in another roost. Seems to be working just fine. If I made the gap small enough to keep the kid out it was too small for the chickens to get in. Goats can't fly so putting it higher seemed like the thing to do.
I can't. Actually, I have two goats living in the chicken run right now, awaiting their date with the barbecue grill.
My goats and chickens eat the same feed (spent grains from the local brewery) so it's not a problem. When I feed the chickens their layer pellets, I scatter them out on the ground during free-ranging time. The goats are generally too lazy to hunt for very many, and the chickens clean them up quick.
The issue I really have though, is the goats eating eggs. Yes, eating eggs. Weird. I notice every so often I'll have a day where there are no eggs in the coop, and that's not normal. It turns out the goats get in there and have a snack!
We have this issue too. We have three seperate enclosures for our barnyard animals (goats, chickens and ducks) but our problem is when we free range them, the chickens need to have access to their nests in the coop. Since I have mini-nubians, they fit through the chicken door.
Is there a way to make a door goats cannot go through that chickens can't? I would need ducks to be able to go through it too.
I have 2 nigerians also and had the same problem. What I did was make a cat sized door within the regular door of the chicken run that the goats can't fit thru. That way I can open up the run so the chickens can come in and out at will without the goats getting in. Don't know how well that would work for little baby goats since they can fit thru such a small opening. The picture doesn't show the little door since I hadn't made it yet but you can get the idea. I just cut out the chain link on the bottom foot or so of the door and attached another fencing panel to it with a smaller chicken size door I can open and close daily. I can try to get a better pic in the daytime.
Part of my problem is the door into the chicken coop has already been cut, nice and large for my large breed chickens, so I can't really make it smaller again.