Go and cross the border to reach Zhuhai city, then take plane from Zhuhai to Changsha and then you may take a long-distance bus to Zhangjiajie.
Route from Macau to Zhuhai Airport: After getting to Gongbei, you can get to Zhong Zhu Mansion (中珠大厦) and take airport shuttle bus. You can hire a taxi if you are in a hurry,.
Airport shuttle bus schedule: 07:00, 9:10, 13:00, 14:40, 16:00, 18:30, 21:00. Ticket fair is around CNY10/person, takes around 1 hour to get to airport.
Route from Changsha to Zhangjiajie: There are no direct bus from the airport to Zhangjiajie. You can take airport bus to get off at Changsha Minhang Hotel(长沙民航大酒店). It costs around CNY 18. There then you may take No.312 bus to Changsha West Bus Station(长沙汽车西站). It takes around 30 minutes. If you take a taxi, it costs around CNY30. Then you can take long distance bus to Zhangjiajie. The ticket is about CNY118. It takes around 3.5 hours.
You can also see the article to view the detail of route from Changsha to Zhangjiajie
2nd Solution: (Flight in Whole Journey)
There is no flight from Macau to Changsha; Flights from Macau to Shanghai are operating by Shanghai Airlines and Air Macau till the end of October. Not sure will they continue to operate them after that. Maybe you can contact them directly for the detailed info.
There are flights from Shanghai Hongqiao Airport to Zhangjiajie.