Sasuke basically uses very little chakra to control Kirin. He merely activate Chidori on his hand and direct the natural lightining towards the opponent as Kirin.
Thats lightning style.
What about Naruto who can can use wind element?
Basically wind is everywhere... Can Naruto uses the surrounding wind to his advantage?
Opp topic: Can Kakashi, Bee and Raikage use Kirin!?