Here's a tutorial for running Fortnite offline on a private server on Linux.
1. Get a private server; I'd recommend something like NeoniteV2 or LawinServerV2 (for this case I'll be using Neonite) with the Carbon Launcher (you need to join their discord server). Be sure to install all of the dependencies (for NeoniteV2 you'll need node.js).
2. Know where your Fortnite folder is located; If you've installed Fortnite through the Heroic Games launcher it should be in ~/Games/Heroic/Fortnite. Keep in mind that for the Carbon launcher to work properly you are gonna have to know what your username is (in my case mash0star) Z:/home/mash0star/Games/Heroic/Fortnite/ is where my Fortnite is located in Wine/Proton.
3. Setting up the Carbon launcher as a non-Steam Shortcut with Proton Forced; Open up Steam and make sure that enabling proton for all games is selected under the compatibility tab under the Steam settings, then add CarbonLauncher.exe as a non-Steam game, then go to the settings and set Proton version to Proton Experimental.
4. Starting up the server for the first time; Open up the Carbon launcher for the first time and set a username. For the path you'll wanna use the path that you got at step 2. You can't copy and paste so just type it out.