Read Values from a Speaker
How could it be destroyed? Voltage is merely 0.15 volts (according to
  multimeter)


If it were 0.15 volts and the speaker was an 8 ohm speaker, the power output to the speaker would be 0.15*0.15/8 = 0.028 watts. Does this seem likely or does it seem more likely that the multimeter isn't giving you the full picture?

If in fact you were driving 1 watt into the speaker, the RMS voltage would be 2.828 volts with a peak voltage of  that is significantly higher maybe 4 to 10 volts for music type signals.

This level of voltage and the level of current that the amplifier output is capable of providing will certainly damage an ADC input on a chip. Next time use a 10k resistor in series and maybe also a coupling capacitor.