As the food delivery driver, Young Ben brings a truck filled with boxes of fresh ingredients as well as certain "special extras" to the prison every Thursday and Sunday. This contraband channel is now something of a family business, as the kitchen supply route has been in place since his father, Old Ben, was the delivery driver.
According to what you heard from other inmates, Young Ben and his family have been able to hold on to this lucrative contract for so long thanks to the rock-solid connections that his father made. Specifically, Old Ben's fishing buddy, Jack, is the younger brother of the city's archbishop, who has certain arrangements with Warden Clark. So even if the kitchen guards do see what's hidden in Young Ben's deliveries, they probably just pretend they didn't.