Is one blockchain of one exchange place the same blockchain used in other exchange places?

As long as your Bitcoins are in Kraken and you haven’t withdrawn them, then the Bitcoins aren’t actually recorded on the blockchain — Kraken just has a line in their database saying they owe you a certain number of Bitcoins.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.