So far, there is no direct flight been launched either from Delhi or Calcutta to Chengdu, but only connecting flights between Calcutta and Chengdu. The connecting flights are available daily and you need to transfer the flight at Bangkok or Kunming. Below is one of the flights on October 26, 2009:

00:40-05:55, Calcutta-Kunming, MU556, China Eastern Airlines
11:55-13:10, Kunming-Chengdu, MU5845, China Eastern Airlines