Once you buy bitcoin, Kraken makes it easy to withdraw your funds and send BTC to any other bitcoin wallet in the world, whether that’s your own or someone else’s. From the Kraken funding page, select your bitcoin asset and then select withdraw. Enter the amount of BTC you wish to withdraw from your Kraken account and enter the bitcoin address (the long string of letters and numbers) set to receive the funds.
It is important to check and be absolutely sure that the bitcoin address you have entered is correct. If you do end up sending funds to the wrong address, even if just one character is wrong, the funds could be lost forever.