Can somebody tell me how much does it cost to go by taxi from Xiamen to Nan An?

Generally speaking, it won't be easy for you to get a taxi to arrive there because of the long-distance. So just hire a private car. The fare would be CNY 300-500 for the single way.
Besides the taxi, you can also choose to take the coach from Fanghu Bus Station. They depart from 06:30 to 18:30. The ticket fare is CNY 26 per person.