To block someone you don’t want to talk to on Kik:
Select Block List
Select the person to block
Tap Yes or Block to confirm
Messages from the blocked person will be hidden and all conversations with this person will be deleted. 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 conversations, your profile picture, as well as changes you make to it will still appear on the blocked person's app.