Blocking someone on Kik Messenger will not delete you from their contact list. They will still be able to view your previous conversations.
When a message is sent from you to another Kik user, the message exists on your device and their device separately. Once Kik servers have relayed the message, they delete it from their system. Blocking a user will not delete the messages that have already been delivered to them.
Kik Messenger was the first product produced by Kik Interactive. It is a cross-platform, customizable, fast-operating messaging app available for most smartphones including iPhone and Android based devices. The first goal of Kik Interactive was a music sharing app exclusively for BlackBerry. Along the way, they accidentally created the breakthrough app Kik Messe.
Of interest, according to Tru Tower 3rd-party add-on Holler!4Kik has been working vigorously on new updates and features and has since changed its name to KTok. KTok brings Kik Messenger more in line with WhatsApp. Find out more here.