Currently, the only official information we have about the Burst Assault Rifle is that it will come in both Epic and Legendary rarities - this seems to follow the example of the silenced pistols and heavy shotguns, which were two similarly enhanced versions of weapons already in the game.
So until Fortnite 4.2 update is set live, you won't be able to complete this task, which is something that needs to be considered straight away. "Due to this delay some quests may not function until the build releases", the support team message confirms.
Epic Games have announced a new release date and time for the upcoming v4.2 update and patch for Fortnite: Battle Royale.
However, even if the Fortnite replay challenge isn't working, there are still a large number of other challenges that you can take care of, though none of them are as easy as watching a match replay would be otherwise.
There's no word from Epic Games as to whether this is an issue that's being worked on, but knowing the studio it won't be long until there's some news, or a patch.
For this reason, Epic Games may choose to wait until tomorrow morning to set the new update live, and avoid rush hour server times.