Is an Airbus A319 allowed to fly with a missing flap track fairing?
Fully permitted according to this Configuration Deviation List for the A320:


  One fairing may be partly or completely missing.




There are more posts about this occurring. As Noah Krasser points out, it looks fairly dodgy to observant passengers. This is the "Master" list, i.e. the safe and approved baseline. Some airlines may have changes in their own internal documents not to dispatch aircraft in this condition at all.