Is there a finite amount of Siege Worms and Krakens?

It is possible to prevent them from spawning, but there is an infinite number that can spawn. Kraken won't spawn on visible tiles, so you can get vision of the ocean to prevent them from spawning. Seige worms spawn from alien nests located on xenomass tiles, so you need to position a unit on, or gain cultural control over, all the xenomass tiles to prevent alien nests from reappearing, and then no more worms will be able to spawn

I am not certain about Siege Worms, but Krakens are certainly not limited. I just finished a game of 320+ turns, and was still killing off Krakens. Unless there was a hidden nest somewhere, they were simply spawning in the middle of the ocean. I would assume the same is true of Siege Worms, although I imagine the spawn rate is much lower than other land aliens.