What does the kitten get?

Solution 1:

Andy F is right - I think you misunderstand what to get it refers to here. This is not entirely your fault, since it is deictic and the actual referent here is not explicitly mentioned (as is usual for this particular use of the phrase).

In this case, get it is being used in this way:

(v) get it (receive punishment) "You are going to get it!" - Source

It here refers to some unnamed but presumably terrible punishment to be meted out to the party in question.

...Put in context, he was joking, really.

Solution 2:

It means the kitten will be killed, and it is a humorous (i.e. not intended to be taken literally) threat similar to (and perhaps derived from) this cover of the National Lampoon from January, 1973:

Although the threats in both cases are mock threats, Jeff Atwood still wants you to upvote questions just as the Lampoon wanted you to buy magazines.

Solution 3:

Here, “to get it” is an idiom that means “to be punished”. In addition, I'll note that there are other related phrases (or variations) with the same meaning:

• catch it: (informal) be punished or told off (American: catch hell).
• get (or catch) it in the neck: (informal) be severely criticized or punished.

Solution 4:

For the record, I'll also provide a serious answer.

The phrase "gets it" in this instance is a term in its own right and is a euphemistic phrase meaning that the kitten will be killed, injured, or have some other form of unpleasantness visited upon him.

Simlar to the phrase "let him have it", which when used in a certain context, means to unleash violence upon someone, the phrase "do (something) or the kitten gets it" is a threat of violence upon the kitten.