Set a pizza stone on the bottom of the oven and preheat the oven to 400°. Spread the baking potato slices on a large rimmed baking sheet in a single layer. Brush with olive oil and season with salt and black pepper. Invert another rimmed baking sheet on top of the first one and bake the potatoes for about 5 minutes, until just tender; transfer to a plate. Repeat with the sweet potatoes, inverting the baking sheet on top and baking for 7 minutes, until just tender.
Increase the oven temperature to 500° and heat the pizza stone for 30 minutes.
On a lightly floured work surface, roll and stretch the pizza dough into a 10-by-12-inch rectangle. Transfer the rectangle to a floured pizza peel and brush the dough generously with olive oil. Arrange the potato slices on the dough and brush with olive oil. Top with the feta cheese and olives.
Slide the flatbread onto the hot pizza stone and bake for about 7 minutes, until golden brown and crisp. Serve hot.