You can view and manage direct messages from the Instagram app for Android and iPhone or Instagram Lite app for Android.
Why can't I find a direct message in my Chats list?
If someone you follow sends you a message, it'll appear in your Chats list.
If someone you don't follow sends you a message, it'll appear as a message request in your message requests inbox. To decline or allow a message request:
When you allow a message request from someone, their future messages will go directly to your Chats list.