Preheat the toaster oven or air fryer to 425 degrees F (220 degrees C).

Whisk eggs and milk together in a bowl; season with salt and pepper.

Heat a skillet over medium-high heat on the stovetop. Add a small amount of oil or butter to grease the skillet.

Pour the egg mixture into the skillet; cook and stir until eggs are set, about 5 minutes. Add sausage, bacon, tomatoes, and mushrooms, and cook until vegetables are soft, about 3 minutes.

Meanwhile, spread the prepared scrambled mixture over the flatbread; top with shredded Monterey Jack cheese.

Place the assembled flatbread pizza in the preheated toaster oven or air fryer.

Bake or air fry the flatbread pizza until the cheese is bubbly and the underside of the crust is golden brown, approximately 5 to 7 minutes.