Place pizza stone or inverted baking sheet in oven and heat to 500 degrees.
Heat 1 tablespoon oil in a large skillet over medium heat. Cook garlic until just tender, about 1 minute. Add chard stems and cook, stirring, until tender, about 5 minutes. Working in batches, add leaves and cook until just wilted, about 5 minutes. Season with salt and set aside.
Stretch dough into a 10-by-14-inch rectangle and transfer to a piece of parchment. Brush with remaining oil and season with salt. Sprinkle with half the Gruyere, then top with chard and sprinkle with remaining Gruyere.
Transfer to the oven: Slide parchment onto stone or baking sheet and bake pizza until cheese is bubbly and crust is golden, 13 to 15 minutes. Sprinkle with pepper flakes.