Can a dentist remove your buccal fat?

Cosmetic buccal fat removal is NOT in the realm of dentists,  They should not perform the procedure.  It's critical to see a board certified plastic surgeon to ensure your best results and minimal risk for complications.  

A cosmetic dentist has training in treating teeth.  Buccal fat is fat which is located in the center of the face surrounded by nerves and salivary ducts.  In most states, a dentist would not legally be allowed to remove buccal fat due to limits in scope of license.  As with any cosmetic procedure, it is better to go to a physician with experience and expertise in the specific areas of concern.  For buccal fat removal, a facial plastic surgeon or plastic surgeon with experience in at least 500 patients would be a good starting point.

Dentist are dental doctors that deal only with the teeth (Dental = teeth). Therefore, they are have no trained or are supposed to do plastic surgery procedures like buccal fat removal.
Oral surgeons, in the other hand, which are dentist specialized in oral surgery could potentially remove the buccal fat since they have training in surgical procedures. 
Asking a dentist to remove buccal fat pads is like asking a veterinarian to treat a children ( pediatric patient). Shoemakers to your shoes!