Is there direct flight from Lanzhou (Gansu) airport to JZG/HL air port?

There is no direct flight between the two places, but the direct bus exists which usually operates from May to October.
It is not suggested to go there by bus with senior people. With senior people, you can fly to Chengdu and then fly to JZG.
The direct bus stops at the entrance of the valley. The food tastes may not be so good in the park. It is suggested to take some food or snacks before you go there.

Thanks, Laura, this is very helpful. :-)
Sorry my third question was a little confusing. I was wondering about accessibility of the scenic spots inside JZG. I know there are shuttles running inside the park. I was just wondering if you have to walk extra distance (e.g. 1 KM) to see the scenes or you can see them right after you get off the shuttles. I am planning to take my parents there, and walking a long distance in the high altitude is my concern. Thanks.

You can enjoy the scenery after your getting off in thge scenic area. But to view more fascinating landscape, you may need to walk dome distance. Don't worry! The road is flat enough.