Two streams on the Tennessee side that are 100% brookies are Road Prong and Sams Creek. Road Prong merges with Walker Camp Prong at the Chimney Tops trailhead just off Highway 441 between Gatlinburg and Cherokee to form the West Prong of the Little Pigeon River. Sams Creek empties into Thunderhead Prong which empties into Middle Prong of Little River on the other side of the park. Sams was just opened up for fishing again in May after a 5-year brook trout restoration project. You can also go up Walker Camp Prong higher up where, at some point (higher than before), the rainbows give way to brookies. If you are going to try Walker Camp Prong, I would get in higher than the Alum Cave Bluff trailhead to Mt. Leconte.
Just keep in mind that the lack of rain this summer has been harder on the streams on this side of the mountains than the Little River watershed.
His eye is on the sparrow and I know He watches me.