In Instagram, you can delete
an entire conversation or just a single message.
These steps work in a similar manner
for both the iPhone and the Android Instagram apps.
Deleting entire conversations.
On the message page,
touch and hold the conversation you wish to delete.
In the pop-up menu, tap "Delete."
Remember that the other person
or people in the conversation
will still be able to see the messages
unless they delete it themselves.
Deleting your own individual messages.
Open Instagram again
and find the message that you want to delete.
Press and hold your finger on the message
that you want to unsend.
When a pop-up menu appears, select the unsend option.
Doing this will delete the message
for everyone in the conversation.