Deliberately Blowing Up an LM386N-4 Power Amp
First of all I am glad safety is a real concern to you. What I am going to suggest will require a ton of it and it's good that you already are aware you could get hurt.

Your suggestion is good: putting an high voltage at the output will exceed the bottom NPN \$V_{CE_{max}}\$ and it will probably fail as a short. That guy down there, together with the other NPN just above is the biggest transistor you can find on the die: plenty of Si to carry your deadly current and to heat the whole die. If you connect terminal 6 and 4 together and apply an high voltage at terminal 5 your result might even be better.

The question is: what kind of power supply are you using? Don't think to put the mains across that thing: your protection switch/fuse/whatever will probably go puff, plus it's not healty for your wires. But what if you use some capacitors? If you happen to have some old ATX psu lying around you can find some 10-100uF 400V caps inside. Hook them all in parallel, charge them to rectified mains voltage and then discharge them on your chip. That will literally blow it up, but the current spike probably won't start a fire. If you have some spare LMs you can give it a try.

Please note that 100uF@400V is 8J of energy. That's more than enough to kill you, capacitors have no mercy. Please, please, please be extra careful if you want to try the capacitor way. To discharge your bank do not use some flying wires, you will need a fat switch or a fatter mosfet. And add a bleeding resistor in parallel to the bank just to be safer.

You can also tear apart an old microwave oven, there is a step up transformer, an HV diode and cap, that should be some 1uF at about 1kV. If you manage to discharge this in the poor LM it really will blast it to pieces. Just be aware that again the charge on the cap is deadly, plus in a microwave oven you can find a magnetron, if you turn it on bad things happen like you becoming blind or impotent.

I am purposely not adding many details hoping to keep the average teen far from this. I once discharged the flash cap of a throwaway camera with a finger and it was quite unpleasant.