1. Right click on the minion and click on the chest icon for linking a food chest.
2. Go <shift><right-click> on a chest with cooked meat in it.
You should receive a message that says you've linked the chest and you can check back at the chest icon in the minion menu.
Every one or two times the minion sells stuff, it should take a bit of food from the linked chest to replenish its hunger.