If the goat is used to being milked, and you are ok at milking, it can only take 5-10 minutes. But, it takes time to get a goat into the milking routine, and it may take longer than that initially. Remember although milking might only take 10 mins, you need to add another 10 mins for sorting out the milk- filtering, pouring it into jugs/ bottles, and washing everything up too!
Beth