If it's a small battery, like a phone, for some airlines, flight attendants are instructed to pick it up with ice tongs and put it in their bucket of ice. The ice/water will cool the fire (removing heat is one method of stopping a fire, as per the "fire tetrahedron," as it isn't possible to remove fuel or interrupt the chemical reaction in most battery fires). Legacy airlines generally have a metal bucket of ice in the flight attendants' trolley, so it's actually fairly useful in that it's on wheels, already loaded with ice, so can quickly be brought to the location of the burning phone. Even there is not enough ice or water in the trolley, placing the burning phone in the metal container can be useful as it will allow the battery to "burn itself out" without catching adjacent materials on fire.
The ability to fight a battery fire like this is the key reason that such electronics are allowed in the cabin and not in checked luggage. But I am not sure what the level of compliance or detection is , do checked baggage x-ray operators look for batteries for example?
