Beijing - Xi'an - Chengdu - Shanghai

Hello, we are looking to visit Beijing, Xi'an, Chengdu and Shanghai. Most of the recommended trips above do not cover Chengdu with these other destinations. What is the easiest way to get from Xi'an to Chengdu and then from Chengdu to Shanghai. We have a few days so are happy to take the train (soft sleeper) from Xi'an to Chengdu, can we book the train trip in advance in the UK or would we need to book when we got to Beijing? Are there flights from Chengdu to Shanghai and what airlines are recommended? Many thanks in advance for your help.