I think his father was Ashkenazi. I don't know where I heard it from. Who knows for sure?
I know his father was originally from Tzfas, but that doesn't say whether he was Ashkenazi or Sephardi. (You normally follow the customs of the father)
On the one hand, R' Kahane went to the Mirrer Yeshiva, which is an Ashkenazi Yeshiva, but on the other hand, I'm not sure if he wore a hat when he davened...
Does Rebbetzin Kahane speak about it in her book?