Train travel from Xian to Changsha and then to Kumning

Well, the trains will be convenient then, but for your first journey, it can be ok to take a high-speed train to your destination from Xian in about 6 h.
But then for your second route, there is no bullet trains, so the ordinary trains will take you about 24h. There are four trains K106, K337, t61, K471 to reach Kunming.