I've searched around to find a solution for getting rid of a couple of years worth of junk / business page / spam messages on Facebook - there used to be a handy Chrome plugin, that's dead and gone. I found a nifty Javascript shortcut that will work. Here's a quick how-to and a link to the JS. 1. Add the "Delete all Facebook messages" link below to your Bookmarks bar so that you can see it, eg;
THIS IS THE LINK [click / drag / drop on bookmarks bar]
2. Go to Facebook and go into your messages view, either archived or main messages window or spam, and then click the bookmark you've created - your address bar may rapidly change a few times. You will most likely get a pop up that says "this will be deleted forever blah blah" and you will most likely have to click the shortcut a few times to get 'em all... better than opening each one and deleting manually.
If you're crap a following the instructions I've penned for you, here's a dude to talk you through it. [and the original link - it worked for me]