how long it takes from Jiuzhaigou to Chengdu by taxis/ car?

The duration is about 7 to 8 hours.
No taxi will run that far. But some hotels provide car rental service. Even if they do not, I believe hotel staff there will be very glad to arrange one for you as they can get some kickbacks.
Generally speaking, the fare is CNY800-1200 based on vehicle types.
If by taking long-distance bus, the ticket fare is about CNY 140 per person. And don't worry. There are some toilet stops along the way.
When will you travel? Anyway, you are suggeated to start off early in the morning, as the road condition may not be that well.