What is the fastest way to reach Zhangjiajie from Chandu?

I think you mean Chengdu?
Well, of course, the fastest way is to take a plane. But there is no direct plan that operates between these two places. You need to transfer at Changsha. It takes around 12 hours including the transfer time.

Or you can take a high-speed train to Chongqing, then a direct flight to your final destination. In this way, the flight duration is only about an hour.