Facebook has the feature to delete all messages within a thread, is it to possible to delete all threads on Facebook, that is, every single message on my Facebook account?
There is no such feature in Facebook, but you can always create a simple Internet-Bot to do it for you. None the less, deleting a message from facebook only removes it from your view and the message would be still available in the account of the other person. So, alternate to deleting your messages, you can Archive them by clicking on the little x as shown in this screenshot:
Or if you do not want to use Facebook any more, you can complete deactivate/delete your account.