You can access Burner's shortcuts by dragging down on the home screen in the app.
Here's a gif to show you what happens when you drag down on the home screen and then change the background color:
Mark All / Delete All
If you are on the tab for a specific Burner, the first two shortcut buttons will read "Mark all as read" and "Delete all messages." Actions will apply for that specific Burner—in these screenshots, the Burners are named Craigslist and Tinder.
If the All Recent tab is selected, the first two shortcuts will instead read "Mark recent as read" and "Delete recent messages". Keep in mind that the All Recent tab includes all communication within the past 7 days.