As of January 2015, there is currently no way to delete an individual message from KIK. However, it is possible to delete an entire chat conversation.
Since it is impossible to delete an individual message in a KIK conversation, the only other option is to delete the entire chat conversation. To do this, select the conversation to delete. Then, simply swipe and delete on the iPhone. For Android and Windows devices, press and hold the conversation, and then select Delete Conversation. When deleting the conversation, it is important to remember that all history of the chat is deleted as well.