So I have never used an IRC chat before so I have no idea what the fuck I'm doing so I'll just post images here.
What do I, uh, do?
IRC is not a unified platform; it is a protocol. What you're doing is connecting to a server (QuakeNet) which would only give you access to QuakeNet's IRC channels. The FES IRC server is entirely separate from QuakeNet.
To use the FES IRC you only need to go to
https://irc.tfes.org/You can also connect with your own client with:
Server: irc.tfes.org
Port: 7000 (requires SSL)
Chat room: #theflatearthsociety
This is all found in the OP of this thread which I highly suggest you read.