I'm not familiar with the kindle, but if you can plug an hdmi into it to show movies on the TV then I don't see why you wouldn't be able to use the hdmi to listen to music too. If you can't, then they have a cable that has a headphone jack plug on each end. One goes into the radio, the other into the kindle.
2013 Jayco Jay Flight 26RLS - 2013 1500 Ram Big Horn
2013 Jayco White Hawk 28DSBH - 2010 V8 Tundra
2012 Jayco X17Z SOLD!:Beerchug: