As far as I can make out there are no direct flights from NRT to Kagoshima (KOJ). However there are quite a few flights from Haneda of which ANA has about 6 daily. If you want to look up the range of available fares and availability, try the ANA website:
http://svc.ana.co.jp/eng/index.html
There's an internet fare which is JPY 24'700.