Is there a procedure to safely handle a PED battery problem on a commercial flight?
FAA Advisory Circular 120-80A contains recommended crew member procedures and training for combating in-flight fires. It has information about causes, indications and procedures of in-flight fire fighting. According to the AC, 


  Upon discovering a fire, the initial focus should be on aggressively
  extinguishing the fire with a readily available extinguisher (which will likely be halon), but do not use water if it is believed the fire is of aircraft electrical system origin. Generally, you should consider using the first available extinguisher rather than delaying your firefighting efforts while you locate a particular extinguishing agent for a class A, B, or C fire. 


Airbus Flight Operations Briefing Notes- Managing In-Flight Fires also says pretty much the same thing:


  Any fire, no matter how small, may rapidly become out of control, if not  dealt with quickly.The first priority will always be to put it out.


Coming to the Galaxy Note 7 issue, the AC says,


  h. What are the Recommended Procedures for Fighting a Lithium Battery Fire? The following procedures are recommended for fighting a fire in a lithium-type-battery-powered PED. The procedures consist of two phases: extinguishing the fire, and cooling the remaining cells to stop thermal runaway.
  
  (1) Utilize a halon, halon replacement, or water extinguisher to extinguish the fire and prevent its spread to additional flammable materials.
  
  (2) After extinguishing the fire, douse the device with water, an aqueous-based extinguishing agent, or other nonalcoholic liquids to cool the device and prevent additional battery cells from reaching thermal runaway.


Though the standard procedures in case of a fire has to be decided by the company, the FAA recommends some procedures to be followed, like:


  • Be aggressive; if flames are visible, fight the fire immediately. 
  
  • Someone must immediately notify the flight crew to describe the fire, smoke, smells, action being taken,  etc.
  
  • If flames are not visible, find the base or source of the smoke.
  
  • Pull circuit breakers, in applicable area.
  
  • Do not reset circuit breakers, unless instructed by flight crew.
  
  • Relocate passengers as necessary.
  
  • Locate hot spots using the back of your hand.
  
  • Don PBE (not necessarily in this order). 


The flight crew (who are supposed to don their oxygen masks on indication of smoke/fire) are supposed to inform the ATC and plan for an emergency landing, if necessary.