Hi, Shenzhen is about 5 hours or so from Chaoan, so I think it is not necessary to take a flight?! If you want to go by air, you should fly to Shantou. Chaoan is not far away from Shantou Airport, you can just take a taxi at the airport and go there. However the point is Shenzhen do not have any flights to Shantou, as I know.

There are no direct flights from Shenzhen to Shantou, but u can take a plane from Guangzhou, but its not cheap (the cheapest I can see at the moment is 620RMB (all inclussive). So I think taking a bus (5-6 hrs) is a better choice. U can also fly Shenzhen to Xiamen, but then u still need to take a bus (3-4hrs). Have a nice trip!