Preheat the oven to 475 degrees F. Cook the bacon in a large skillet over medium heat until crisp, about 10 minutes. Remove with a slotted spoon and drain on paper towels. Add the tomatoes to the drippings in the pan and cook, turning once, until slightly softened, about 2 minutes.
Brush a large rimmed baking sheet with olive oil. Stretch the pizza dough to fit the pan (if the dough shrinks back, let it rest a few minutes before continuing). Prick the dough all over with a fork. Top with the tomatoes, reserving the bacon drippings. Bake until the crust is golden brown, 12 to 15 minutes.
Remove the flatbread from the oven; top with the goat cheese. Season with salt and pepper. Toss the sprouts and arugula with 1/2 tablespoon of the reserved bacon drippings (rewarm, if necessary), the lemon juice, and salt and pepper. Top the flatbread with the greens and bacon.