This tutorial explains how to delete individual conversations or messages in the Facebook Messenger app.
This procedure applies to iOS, Windows Phone, and Android.
Delete a Conversation in Facebook Messenger
Open the Facebook Messenger app, and find the conversation that you'd like to delete. Tap the Menu button, and then select the Delete option:
The conversation thread will be deleted in its entirety.
Delete a Message in Facebook Messenger
Open the Facebook Messenger app, and select the desired conversation.
Hold your finger down on the message that you'd like to delete until a small menu is displayed. Select Delete from the menu options: