Best way to make LEDs flash in time with a music source
There's a website for analog audio circuitry that I really like: https://sound-au.com

In keeping with the author's request, I've only provided a link to the home page, but if you add these to the end of the URL, you'll get:


/project60.htm


LED volume meter

/project136.htm


Real-Time Analyser (RTA), basically a full spectrum of what's happening at the moment

/project62.htm


Complete lighting system, including a "Sound to Light" (S2L) module at the bottom of /project62a.htm



Perhaps you could adapt one of those?



Or if all you want is to flash a single LED in sync with, say, the kick drum, then you could use a dual opamp to:


Lowpass the signal so you're more likely to trigger on the kick rather than the hihat 
Compare the result to some reference level


The result of that can either drive the LED directly if the opamp is strong enough, or feed a transistor.