How do you permanently delete Instagram messages?

These are the steps to deleting an entire conversation:
  1. Tap the inbox button at the top-right corner of your home screen.
  2. Choose the conversation that you want to delete. Drag it to the left.
  3. Tap Delete.

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How do you delete Instagram messages on both sides?

Simply hold down your message and tap on “Unsend”. This will delete a message from both sides, so the person you send it to won’t be able to see it anymore. That’s it! The message will be deleted from both sides.