We are aware that some Xbox One and Xbox Series X/S players are currently having issues logging into Fortnite. We are working on a fix, but in the meantime please close out of and relaunch Fortnite, and make sure you have downloaded the latest update.
As a temporary workaround, we've found being connected to the network via wired Ethernet and not over wifi can bypass this issue.
For updates, please check our Twitter Status account: https://twitter.com/FortniteStatus
Let us know how we can help you.