Dentists do not have the same amount of medical knowledge as physicians. We learned anatomy, biochem, pathology, etc in dental school and never use it again. Just as a medical student who learns dental anatomy and occlusion does not know as much about dentistry as a practicing dentist. There are internships, rotations, residencies and clinical experience that an individual goes through to gain the knowledge to practice medicine. It's more than gross anatomy and physiology. A competent oral surgeon is much more qualified than a dentist...
That being said, if someone fainted, are they breathing? Do they have a pulse? If no, cpr and have the flight attendant get the AED (all US airlines have one on board). If they have a heart beat they have a chance of living until help arrives. There is a medical kit on board only to be dispensed to an MD. Not sure if they would even let you see it if you told them you are a dentist.
I was an airline pilot before I became a dentist, so I can tell you that at this point the pilots have declared a medical emergency and are diverting the flight to the nearest available airport with medical services nearby. Depending on where the flight is they can patch through to a doctor (usually at a university hospital) to assess the situation from the ground.
Make sure they have a pulse and are breathing, try to stabilize the pt until the plane is on the ground and let the professionals take over.
