Spoon the greek yogurt into a fine mesh sieve set over a bowl. Transfer to the refrigerator and allow to drain for at least 1 hour.
In a spice grinder, process the thyme and lemon zest until finely ground. (If you don’t have a small grinder, you can skip this step. Your mixture will just be a bit coarser). Transfer to a small bowl and stir in the sesame seeds. Set aside.
Place an oven rack in the top third of the oven and turn the broiler to high. Brush both sides of the flatbreads with 2 tablespoons of the olive oil and sprinkle with kosher salt. Arrange in one layer on a baking tray. Place the baking tray under the broiler for about 1 minute, or until the tops are just starting to brown. Remove from the oven and flip the flatbreads over. Top each one with equal parts of the yogurt, spinach, sliced red onion and feta and sprinkle with the thyme mixture. Place back under the broiler for about 2 minutes or until the spinach has wilted and the edges of the flatbreads are golden.
Remove from the oven and drizzle the flatbreads with the remaining 2 tablespoons olive oil. Serve immediately.