What is the best way to travel from Singapore to Meizhou? I heard there is flight from Guangzhou?

Yes, you can fly to Guangzhou first. Then change the flight to the destination.
The distance between airport to Dabu is around 80km. Upon landing, you are suggested to take a taxi to Jiangnan Bus Station first. The cab fare is around CNY15. Then there are many buses to Dabu. The bus schedules are from 06:50 to 18:00.