Preheat the oven to 450°F. Line 2 baking sheets with parchment paper.
Combine the flour and yogurt together in a bowl; the mixture will be clumpy. Transfer onto a clean smooth surface and knead the dough until it is smooth and can easily form a ball, about 5 minutes. The dough will become less sticky as it is kneaded, but if the dough is sticking too much to your hands, add only a sprinkle of flour at a time onto the dough and continue to knead until smooth.
Once the dough is kneaded, divide it into 4 equal-sized pieces, and form those pieces into balls.
Form each flatbread by rolling each ball out into a circle about ¼" thick. Drizzle oil on top of the parchment-lined baking sheet, and place the rolled out flatbread onto the baking sheet; 2 per baking sheet.
Brush the flatbread with olive oil and sprinkle generously with za'atar and flake salt.
Bake the flatbread for 10-12 minutes, or until puffy and golden brown. Remove from the oven, allow to cool slightly, and serve with dipping sauce.