To "milk something" (sometimes seen as "milk it for all it's worth") is to keep pushing well beyond what you would normally have expected. For example, perhaps your cable company is a local monopoly and nails you with fee after fee after fee, so the apparently-low rate isn't so low after all; they can be said to be "milking" their customers. It works for non-tangibles too; say you've had a minor disagreement with somebody, but in telling the story to your friends you exaggerate the emotional harm to you; you're "milking" the situation.
"Got milk?" is an advertising slogan from, yes, the milk industry. "Get milked" is a play on that.