Explantation for fried charger with Multimeter
As others have said, connecting a multimeter set to measure Amps directly across a power supply effectively puts a short circuit on the supply, due to the very low resistance of the multimeter when set to measure current.  The short-circuit current you measure this way will probably be far above the supply's rated output, unless the supply has overcurrent protection.

I don't think it is practical to try to verify the rated output current of a power supply by a direct measurement - you just have to trust the maker's claim.

You could, however, connect a load of the correct resistance to draw the rated current to the supply, and monitor the output voltage and power supply temperature over an hour or two to see if the supply survives, and continues to output the advertised voltage, and doesn't get too hot.