Once you have it set up, I'd say no more than about 2 hours per week. The feeding and watering can be automated, so it's really just whatever cleaning or optional shuffling of their locations you do. Checking for eggs can be done in a few minutes, and you technically don't have to do it every single day. You might actually choose to spend more than the minimum to tame them and treat them as pets.
Yeah, I'd say two hours a week, maybe an hour. Feeding and watering and checking for eggs can be done quite quickly when it's below freezing out :)