Toss the broccoli with 3 tablespoons olive oil and the red pepper flakes on a rimmed baking sheet. Sprinkle with salt and pepper.
Mix the tomatoes with the garlic in a small bowl. Sprinkle with salt and pepper.
Roast the broccoli until it begins to turn brown, 16 to 18 minutes. Add the tomatoes to the baking sheet, then toss with the broccoli and roast until tender, about 6 minutes.
Meanwhile, divide the flatbreads between 2 baking sheets. Top with the mozzarella, leaving a 1-inch border, then top with the broccoli and tomatoes. Sprinkle with the olives and pepitas. Brush the edges of the breads with the remaining tablespoon olive oil.
Bake until the mozzarella is melted and the flatbreads are very warm, about 8 minutes. Drizzle a little olive oil on the tops and sprinkle with more red pepper flakes if you like it spicy. Cut into wedges and serve.