Are there nonstop flights from Kagoshima (KOJ) to Osaka (KIX)?

Yes. Peach fly this route. Flight time is about 1h 6m.

What is the fastest connection from Kagoshima (KOJ) to Osaka (KIX)?

via Fukuoka ≈ 1h 46m, via Amami ≈ 2h 27m, via Tokyo ≈ 2h 36m (estimated flying time, excluding layovers).

from 13,000 ANA miles, from 15,000 JAL miles (economy, one way, based on the published award charts).

Kagoshima Airport (KOJ) to Kansai International Airport (KIX)・512 km

Nonstop flights available (1 airline). Flight time about 1h 6m. Nonstop return flights also operate.

With milesANA 13,000 miles+ (via HND)JAL 15,000 miles+ (via HND)Economy, one way, estimate. Tap a connection for miles by cabin.

4 one-stop options, sorted by estimated flying time. Tap one to see the airlines on each leg and booking links.

Times are estimated from distance. Check schedules, frequency and availability with the airline or a booking site.