Originally Posted by Pseudo Nim

They should be able to check your bag through. 20 minutes is usually ample time in small Japanese airports (I've had 10-15 min connections), but if you do need to get your bag out then you should probably allow around 40 mins to go out, get bag and go back in. But I'd feel confident they can check my bags through.

Originally Posted by CPH-Flyer

They should be able to check your luggage through. While a different airline, it is still part of the JAL group. Kagoshima airport only requires passengers to pass through immigration 15 minutes before departure, so 20 minutes MCT seems within reason as long your baggage is checked through.