For Android users, the notification settings are within the app; for iPhone users, push notifications are controlled from your phone's main settings section, and app notifications are controlled from with the app.
For Android users only:
Notifications are free but you can disable them via your notification settings the app. In the left menu, scroll to "Settings." Look for the "Push Notifications" and "New User Notifications" buttons. We try to send notifications only when we have important news. This setting will disable all notifications including our system notices about expiring kick bonuses, rewards, and more.
For iPhone users only:
Push notifications can't be controlled inside the shopkick app. Go to your phone's "Settings" section, look for shopkick and change the notifications there. App notifications (or "New User Notifications") can be toggled on and off within app settings.