Thanks to Roderick Leyland (7.04):

Pig's Milk: According to Swine Management and Nutrition on the web, someone
replying to a similar question advises it's not possible to milk, breed,
farrow and remove the baby pigs to milk the sow.

There is also a short correspondence on ThePigSite.com. Someone has milked a
pig but you don't get much.

I like bacon but if I saw a product marked 'Cooked with pig's milk' it might
put me off.