There is a very good spring on your way out of the Shinning Rock "Campground" toward Flower Gap and Tennant Mountain. The spring is just beneath the trail and turns into a nice size stream.
We did a water drop at the Black Balsam parking lot since one of our people was heading out there. The next two reliable sources were the springs at the two shelters after you cross the Blue Ridge Parkway.
The trip was amazing and we want to get back there. It is somewhat dry up there so be ready to carry some water.