I've just reached Pirate Legend and I've still yet to see a kraken, given the amount of hours put in I'd expect to see it at least once.
I'll never unlock the cosmetics associated with beating it.
The kraken encounter is part of the world event cycle. As soon as a world event is completed or despawns, the kraken start looking for a prey.
So the fastest way to get a kraken would be to get in a server with ships completing world events, then pray to the Sea of Thieves gods that they’ll finish the event while you’re in deep water and kraken chooses you as it’s prey.
So basically a Kraken only attacks when no world events are active. If you see a Fort, Flameheart, Skeleton Fleet, or Ashen Winds, there is no chance for you to get Krakened. When a world event ends, the Kraken starts looking for prey. You will need to be in open waters, away from any islands. It will attack one ship, and then it's gone. Another world event starts, and the cycle repeats. So if you are in open waters when a world event ends, with the current maximum of 5 ships / per server, chances are you are probably getting attacked. So to answer your question, this is the only thing you can do. The rest is up to the Sea of Thieves RNG Encounter Gods.
@sirhumongous really!? I get Krakened all the time have a bunch of loot on your boat and sail in deep water when there's no world events