I don't know much about goat diseases, but it seems many people I know commonly have both chickens and goats together. Worms and diseases such as coccidiosis are usually species specific, meaning they shouldn't infect each other. If I were you, and you don't receive more answers here, then I would simply Google "common goat diseases" and "common poultry diseases," as well as "can goats and chickens be kept together?"