Chongqing enjoys almost the same importance to Tibet flights as Chengdu. It manages flights with Lhasa departing every day which will take about two and half an hour.
Flights to Xining from Chongqing Airport run several times a day and take just two hours. Most of the Chinese internal airlines run flights, and the prices range from US$206 and up, for a one-way flight in economy class. It is recommended to pre-book your flights, as there can be limited seats available on the flights if you are trying to buy your tickets on the day of travel. Searching the internet for available flights and the best prices will help you to get a cheaper flight.
There is lots of advantage of traveling via airplane to Xining and then taking the train from there. It is that you can save time on the trip. Another way as Xining is at an elevation of 2,275 meters, you can always spend a day there to help with acclimatizing to the higher altitudes. This can help to reduce the risk of altitude sickness. Moreover, as most of the spectacular scenery is on the train from Golmud. (where the train starts its ascent to the Qinghai-Tibet Plateau) you would not be missing any of the best parts of the train journey.