Any flight from xiamen to shantou, if not how much does it cost to travel by rented car.

No flight between the two places. There are many buses between the two cities everyday. You can take the long distance bus to reach. Renting a car will be expensive, because this trip will cost you about 4 hours.
There is no car rental service there to drive to you Chaozhou, but the buses are very frequency. So you do not worry.