How do I delete a conversation in Instagram Direct?
To delete a conversation in Instagram Direct:
Instagram app for Android and iPhone and Instagram Lite app for Android
  1. Tap direct or messenger in the top right of Feed.
  2. Swipe left (iPhone) or tap and hold (Android) on the conversation you'd like to delete.
  3. Tap Delete, then tap Delete to confirm.
Once you delete a conversation, it will no longer be visible in your inbox. Keep in mind that this only deletes the conversation for you, and that it will still appear for other people included in the conversation.
Note that your Data Download file doesn't include messages that you've deleted from your Instagram account.
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