There are now direct international flights from Hong Kong, Paris, Seoul, Singapore and Tokyo to Chengdu. The distance from Beijing, Shanghai to Chengdu is more or less equal with many direct domestic flights.
Airfare can be expensive, especially if you book any direct connection to Chengdu. The least expensive way to travel to Chengdu from abroad is to fly into Shanghai or Beijing and buy separate round ticket to Chengdu from the Chinese travel site: english.ctrip.com (Note fares on this site is priced in Chinese Yuan CYN).
International fares in the summer are expensive, especially booked well in advance. The prices normally come down somewhat if booked a little less than a month before the departure dates. You might want to keep this in mind if you would like to keep your travel cost down.