It is a shed (8ft by 10ft). There is two runs we have as well. The one attached to the coop is 8ft by 16ft.
My feeling is that that is too small, but I have never had dwarf goats.
I was thinking about it, and came up with a few problems.
1 I'm not quite sure how big he is, but there is a definite possibility the chickens could injure the goat. Like wise, could the goat injure the chickens?
2 This is a big one, how would you keep the goat out of the chickens food? If your chicken food has got any meat in it (quite a lot do, it should say on the back of the sack) it is a big no no for a goat to eat it.
Even if it doesn't, he still shouldn't eat it, as chicken food is formulated differently from goat food.
3 I know both chickens and goats can get coccidiosis, but what I don't know is is it the same form of it? If it is, you may have problems with the goat catching it from the chickens.
Maybe someone else can commented on that.
My overall feeling is that is a bad idea, but that doesn't mean its impossible, and in the right set up could work well?