There are two places to check to make sure that notifications are enabled. The first is within the Blink app. If you hit the menu in the top left-hand corner of the app, and go to "Manage Account," there will be a "Notifications" tab. The first thing to check would be to ensure that all the notifications you wish to receive are enabled in the Blink app. A picture of this can be seen below:
The second location, as you mentioned, is within your device's settings. Under the "Sound and Notifications" menu you want to ensure that the notifications are allowed within the Blink App, and not disabled.
If this doesn't solve the notification issue, or you need anymore assistance, please let me know!