To block someone you don’t want to talk to on Kik:
Select Chat Settings (on your iPhone or Android) or Privacy (on your Windows Phone, Symbian or BlackBerry)
Select Block List
Select the person you want to block
Tap Block to confirm
Messages from the blocked person will be hidden and all chats with this person will be deleted. The blocked person won't be able to add you to any group chats. Also, when the blocked person tries to send you a message, they don't know that they are blocked and their message is never delivered to you.
However, previous chats, your profile picture, as well as changes you make to it will still appear on the blocked person's app.
See the FAQ on managing messages from new people to learn how to use the New People feature