Follow the Green River trail south for upwards of 14 miles to Three Forks Park which is a large grassy meadow about a mile long. Pick up a small boot path through the grasslands and marshes and cross the gentle Green River (will require wading through waist deep water). Continue climbing up the grueling Tourist Creek drainage. With route-finding, this drainage never exceeds class 2 hiking. Stay on the right side of Tourist Creek as long as you can until you get to the first tarn (good camping). There are many places where hopping over large boulders is necessary and a misstep can result in serious injury especially with a large pack on your back.
Continue up the creek as it slowly mellows and pass by 3 or 4 small tarns. Crossing Tourist Creek a few times enroute. Pass by a side stream coming down from the right and crest a small rib between the creek and an unnamed lake. Once you get to the base of the headwall, which is a steep talus slope, ascend it stating towards the right side where the slope isn't as steep then cutting back left. This slope is very loose so caution should be taken. You will eventually get to a low spot on the continental divide at a saddle between Klondike and Pedastal Peaks. Keep in mind that it can take days just to get here for anyone not in perfect shape.
From the saddle start climbing to the right (south) up the slopes along the continental divide up to the summit of 13,340 Pedestal Peak. These slopes are fairly gentle and require no more than class 2 hiking. As you near the summit you may pass by a glacier research pole that says not to touch it. I was amazed to see this which meant people had been there. The summit area of Pedestal actually has many small flat-topped rock towers that look like pedestals. The true summit was at the top of one of these pedestals which required a class 2+ move.
The views atop Pedestal Peak are spectacular. To the south Flagstone Peak seems to attack you while to the north an endless sea of gentle continental divide peaks demands attention. From Pedestal, begin descending towards the 13,060 saddle between Pedestal and Flagstone. This descent requires a couple easy class 3 moves but nothing remotely very hard. Once at the saddle climb to the summit of Flagstone and enjoy one of the most remote summits in the Wind River Range! Re-climb Pedestal and descend your ascent route of Pedestal. There is no red tape whatsoever in this wild and unspoiled wilderness however it's good to practice leave no trace techniques. Camp only on durable surfaces and avoid making fires above treeline.