'Milk' in its literal sense is what farmers do when they take milk from their animals. If you 'milk a cow' you get milk from it. You're right in thinking that it is an idiom in this sentence. If you 'milk' a situation you exploit it as much as possible for as long as possible. If you 'milk a joke' you tell it many times, or stretch it out for as long as possible, in order to get as many laughs as you can out of it.

Hi there Jessica! My name is Autumn and I hope I can help answer your question. :) So the word "milk" is used most often as a noun. But, on occasions it can be used as a verb. As a verb it is most often used like this..."She milked the cow." When the word is used in this way, it means, "To get the milk from an animal." So whether you're milking a cow or goat, etc. it means to get the milk from them. But when it comes to the way that you encountered it, it can mean "to draw out, to make last longer." It can also mean, "to exploit, or to defraud." When people talk about "milking a joke, " it means that the person who told the joke continues to use and perhaps even overuse, but even though the person who is telling the joke is using the joke continually, the joke still stays funny and fresh. So, when milk is used as a verb in the way that you encountered it, it's saying that the person is drawing out something, and yet at the same time, it never gets old or boring. It stays fresh. All of this has been my experience with this word, and I hope that it's been a help to you. :) Good luck on learning English (as a native speaker I know that it can be quite a fun and rewarding language to speak :)). Have a great day! Autumn :)

idiomatic expression ? - yes , it is . We all know what it is to milk a cow - that is using your hands to squeeze the milk out of the udder to the last drop . So , figuratively speaking , to milk a joke means to maximise the effect of the joke as if to the last drop . eg Be careful of him , coz he will milk you dry ( empty your pocket )