If you have messages in your Facebook inbox, I’ve got the technique to delete them using VoiceOver.
Go to your messages area on Facebook for iPhone application. When you swipe to a message, instead of double-tapping, double-tap and hold for a few seconds. You can move your finger if you wish, a little window will come up. Double-tap on “confirm deletion for “.
Good luck!
Source Article from http://www.applevis.com/guides/deleting-messages-facebook-ios-app