At this time, there is no option to delete a Private or Public Group you have created. You do, however, have the option to leave your Group.
To leave your Group:
- In the Kik app, select your Group chat
- In the chat, tap the Group name at the top of the screen
- Tap on Leave Group
- A pop-up message will appear where you can confirm and tap Leave
Once you leave your Group, ownership will be passed on to a random Admin. If no Admins exist in the Group, ownership will be passed to a random member instead.
To learn how to create a new Private or Public Group, go here.