Why does LED flicker and buzz?

I got the new fixture installed over the bathroom vanity and put in LED bulbs. One is fine but the other flickers and buzzes. Replaced those with two incandescent bulbs and they are fine. I am confident in the wiring connections. The light switch is not a dimmer but it is old - could that be the source of the problem? Any other possibilities?

Don't know if this link to video of the light will work but worth a try: New video by Tom S