1. Connect by address
Multiplayer, Connect to address, with the address and port from the dashboard. If that works, the server is up and the rest of this list is about the public list.
2. The factorio.com token
A public server needs your factorio.com username and token in server-settings.json. Without them the log says "Matching server connection failed: Error when creating server game: Missing token." and the server is not listed. On Flux, add both in Server Settings.
3. visibility.public
It must be true. It is in the default file.
4. Your version
The public list only shows servers your version can join. A player on an experimental beta does not see stable servers, and the other way round.
5. Password and filters
The list can hide servers with a password; check its filters, and search for the exact name.
Frequently asked questions
Why is my Factorio server not in the public list?
Almost always a missing factorio.com username and token in server-settings.json. The server still accepts players by address.
Where do I find my Factorio token?
On your profile page on factorio.com, after you log in. It is not your password.