This wall has three rarely climbed routes. Most people that are this far into the park usually keep going to Windy Point. I only included Winged Messenger as it was the only route that had enough info to warrant an entry/only one worth climbing.
Go up through the gap to the left of Tarzan, walk through the gully on the other side and up through the gap in the next rock. First route is on the right.
Mountain Project's determination of some of the classic, most popular, highest rated routes for Flying Buttress:
Shiprock stands by itself from the main cliff area. Stay to its right going past Tarzan, Silk road and OTC. Follow a minimal trail up river crossing a small gully. Keep walking for about 200 yards turn left and you should see the cliffs. Work up hill on the north side of the formation for Winged Messenger. Bolts can be a bit hidden, but are there.
For a spicier approach follow the gully left of Tarzan. From the top of the hill you'll see Flying Buttress just ahead. Once through the gully keep close to the wall on your left and continue past the steep basin on your right. At Flying Buttress you'll have to scramble up into the fissure separating it from the main wall. Walk out from between the walls and check out one of the finest views at Pictured Rocks. Scramble down a bit and you'll find Winged Messenger to your right. Lots of steep hillside. Use caution.