Hi, as I know, there are several flights from Manila to Hong Kong, China everyday. So you could fly to Hong Kong firstly and then trafer to Chengdu by air. When you arrive in Hong Kong Airport, you could also take a ferry to Shenzhen Airport quickly. At Shenzhen Airport, you could take a domestic flight to arrive in Chengdu, too.

The flight infor could be searced at https://www.travelchinaguide.com/china-flights/