I have received the email from JR West. They confirmed Japan Rail Pass can be used for Kyushu Shinkansen. But Japan Rail Pass can be used for only Sakura that is the second fastest train between Shin-Osaka and Kagoshima-Chuo. We cannot take Mizuho that is the fastest train between Shin-Osaka and Kagoshima-Chuo by Japan Rail Pass. JR West and Kyushu applied same fare table as Nozomi. So Japan Rail Pass does not cover even the basic fare. If you take Mizuho, you have to pay the full fare.
Of course we take Tsubame that is operated between Hakata and Kagoshima-Chuo. If you cannot take Sakura, you can take Hikari or Kodama to Hakata, then transfer to Tsubame.
If you want to see the images of trains’ interior, please see the post, N700 series for Kyushu Shinkansen Mizuho and Sakura