Hello,
I had this problem in Firefox, too:
Firefox seems to not allow video and audio to play without the user interacting with the site at least once (clicking onto an empty area is enough).
Giving Kagi "Autoplay Audio" or "Autoplay Audio and Video" permissions in the shield icon left to the address bar resolves the issue.
It'd be nice if Kagi could somehow either request this permission so Firefox shows a dialogue (if that's possible) or have a pop-up tell you how to give the permission yourself.
I almost burned my bread because I didn't hear the timer ring XD