I noticed that you can connect to Twitch.TV channels via IRC following the instructions here. I was happy to see they even had specific instructions for KVIrc. What I was unhappy to see is that it wouldn’t work because of my user name.
On IRC, nicknames beginning with numbers are not allowed. So, KVIrc refused to let me put “3vi1” in the nick field as per the instructions. I got around it by putting a temporary value (_3vi1) in the server configuration, closing KVIrc, then editing .config/KVIrc/config/serverdb.kvc to contain 3vi1.
After that, it connects fine!