With chrome extension you can simply delete all the Facebook messages with one click permanently.
How to Delete a Facebook Message
Clicking on the archive button wont delete messages permanently.When the person sends you a message ,you can see all the messages in the archive.
To delete Facebook messages permanently,go to Actions–> click on the delete message option.
But this is time taking process.
How to delete all Facebook Messages at once
Add a extension to Google Chrome.It allow you to delete all your messages at once.Click here to add the Chrome extension.Just activate the extension and log in to your facebook account.Now you can delete all your messages very easily.