1. Preheat oven to 400ºF. Arrange racks in top and bottom thirds of oven. Line two baking sheets with foil. Place one flatbread on each baking sheet and brush each with 1 Tbsp. oil. Bake until puffed and lightly browned, 4 to 5 minutes. Repeat with remaining flatbreads.
2. Top each flatbread with olives, artichoke hearts and red peppers. Scatter goat cheese on top of vegetables. Bake until cheese is softened and pizza is hot, about 10 minutes longer. Serve immediately.