How to supply 5 to 12v amplifier LM386
A 9V output from a transformer will be alterating possibly up to a peak of 13 Volts and down to a negative peak of -13 volts. It will be doing this 50 or 60 times per second and I'd bet on the first negative cycle from the transformer you burned the chip and possibly damaged any electrolytic capacitor on the module.

I'd throw it in the bin and get a new one. Welcome to the learning process. Next time, add a bridge rectifier and smoothing capacitor and measure with a voltmenter to make sure polarity is correct and the dc voltage level.