As long as your Bitcoins are in Kraken and you haven’t withdrawn them, then the Bitcoins aren’t actually recorded on the blockchain — Kraken just has a line in their database saying they owe you a certain number of Bitcoins. You wouldn’t find this on the blockchain until you actually initiate a withdrawal of your Bitcoins from Kraken.
Every Bitcoin exchange, and every Bitcoin user in the world, when they do publish to the Bitcoin blockchain, publish to the same blockchain though.
