Kraken ships can be unlocked to build for a limited time by participating and winning a Kraken building with your alliance when Kraken Fracture event opens. Look out for it to show up on the right side of the screen every week or two to know when it's coming up.

Also during the Kraken Fracture event, there will be small Kraken fleets that appear around the galaxy map. These fleets can be found and destroyed, and have a chance to drop Kraken build chance items. These build chance items give you a chance to build a small amount of Kraken ships. Of course, winning the Kraken buildings in the event is much better as these give you no limit on how many ships you can build during the allowed build time!