Open Instagram
Tap the Messages icon
Open the chat you want to delete
Tap and hold the chat on the inbox screen
Select Delete
Confirm Delete
To delete one message you sent
Open the chat
Tap and hold the message
Select Unsend
To delete a conversation on iPhone
Swipe left on the chat in your inbox
Tap Delete
To delete a conversation on Android
Tap and hold the chat in your inbox
Tap Delete
To delete all DMs
Delete each conversation one by one