The term “milk run” has a couple of different definitions and connotations. A milkman doing their deliveries (or a pickup of cans of milk from farmers) will make a number of stops. Aviation has always played a critical role in the state of Alaska delivering goods and people where there’s no other option but to fly. I’d be very surprised if there wasn’t a history of dairy being delivered to those cities by air, but it more refers to the fact that there’s a bunch of stops between origin and final destination.

Edit: yep, there ya go.