As I understand it it's the anti-cheat that is the problem. If this is the only problem there is essentially only two possible ways to get Fortnite running in Linux:
- Get Epic to support Linux
- Crack the anti-cheat.
Since a major part of anti-cheat systems is preventing people circumventing it I would say that the easiest path would be getting epic to support Linux. One valid argument would be to play Fortnite on Steamdeck .