How do I manage messages I’ve received with Instagram Direct?
When someone you follow sends you a message with Instagram Direct, you can view it by tapping 
If someone you don’t follow sends you a message, it’ll appear as a request in your inbox. To decline or allow the message, swipe left on the message (iOS) or tap and hold the message (Android) then select Delete or Accept. You can also tap Delete All at the bottom of the screen to ignore all requests at one time. When you allow a message request from someone, their future messages will go directly to your inbox.
Learn more about reporting abusive messages.