Microsoft has released today a new update to the Outlook Mail and Calendar app on Windows 10 Mobile which brings quick actions on notifications to the production ring (via Windows Central). To use this handy feature, you’ll first need to turn on notifications banners in the settings. Once you get a new notification, you can just swipe down on it from the home screen to display the two quick actions buttons. If you missed the notification banner, you can still access the quick actions in the notification center.
Quick actions can be configured in the settings (those quick actions will be the same than the in-app swipe actions) if you want to change the default options which are "Delete" and "Set flag." To try this feature, make that you have downloaded the latest version 17.7466.41148.0 of the Outlook Mail and Calendar app.