Let's look at it like this:
Kakashi himself said that pure chakra attacks are much stronger when they have both shape recomposition and elemental recomposition.
Chidori is lightning chakra in the shape of a sword. It's got both shape and elemental recomposition.
Rasengan is a ball of raw chakra. It's got just shape recomposition.
Rasengan is stronger than Chidori, even though it doesn't have elemental recomposition.
And Kirin is just raw lightning. It's not particularly strong, it's just virtually unavoidable. All of these attacks (Chidori, Rasengan, Kirin) could kill you on one hit.
In that sense, Kirin's not much stronger, in plain old power, than Chidori. While I wouldn't go so far to say that a plain old rasengan could stop Kirin, I would say that a Kuuton: Rasengan would. And if that's true, a Fuuton: Rasenshuriken would definitely stop Kirin.