Common Summer Wildflowers in the Smokies. Wood Sorrel NPS Photo. Flame Azalea NPS Photo. There are over 1,500 kinds of flowering plants that grow in Great Smoky Mountains, more than in any other American national park. Flame azalea is a flowering deciduous shrub that blooms at low elevations in April and at high elevations in June and July. The leaves and flowers are concentrated at the end of the branch, and the flowers are red and yellow. Flame azalea is commonly seen throughout the park.