To remove Live activities from iOS and Live notifications from your device,  please go to your home page where you see the notification and swipe left to clear it. This works for both iOS and Android devices. Alternatively, you can also go back to the flight you're following and tap the Follow button again. This will remove the Live activity/Live notification from your screen. A third option is to tap the Live activity/Live notification after the flight has ended which will result in the notification being removed from your screen. 

To completely disable the Live activities and Live notifications functionality, you should go to Settings > Misc and disable it from there. See our screenshot below for more information.