Not legal advice: In Kik's legal disclosure they say that conversations are only stored on your mobile device and on the mobile devices of those you engage in conversations with. Kik only records the message sender and recipient data. Any messages are usually deleted by the app right away after they have been delivered to the intended recipient(s). Messages not delivered may stay in Kik's system.
Kik also says that if you agree to use their services there is a possibility that any messages they have on file can be released to authorities if warrants or subpoenas demand them or if you are threatening or abusing other app users. Kik is not secure. Recipients can save, store and share any messages you send them.
Of interest, Kik recently announced that it has hit 50 million registered users.
Sadly, the messaging service was just linked to an alleged indecent assault and an alleged child abduction in North Texas.