2 layovers in China, less than 24 hrs total

I'm a US citizen looking at a ticket that transits through China. I arrive in Beijing ar 6:40pm one day, have a layover for a couple of hours then fly to Kunming where I have a 16 hrs layover. My next flight to KL leaves at 5:40pm. Am I eligible for the 24 hrs visa free transit? And can I leave the airport in Kunming?