Can you have a draw in Fortnite?

Solution 1:

No, there are no draws, there is always one winner

It is also impossible for the last two people to die "at the same time" because of latency, the server will know who died first, or at least it will know who's "I died" packet reaches the server first

If you want to do some reading, here is a form post: https://www.epicgames.com/fortnite/forums/battle-royale/royale-with-cheese/113641-is-draw-somehow-possible

Solution 2:

There is only one exception that I've encountered and that is the current 5 teams of 20 also known as the Final Fight mode. In this mode the winner isn't the team that has survived while others are dead, but the game ends after some time in the third and quite small circle. When the game has ended the team with the most players left is the winning one (downed players count too). There are multiple times that I've been on the winning team when the clock has run out and I've gotten 'victory royale' while our and an enemy team had as many players left in the game. Therefore I assume that the rules allow draws in this particular mode.

The Express seems to confirm my assumption saying:

Once the timer expires, the team with the most players wins—and, in the event of a tie, the two teams (or more) tied in first place share the spoils.

In all other modes there is no draw ending possible as they end in all other players in other teams dead.