Position the oven rack in the top third and preheat the broiler to high.
In a small bowl, whisk together Frank's RedHot sauce, white vinegar, garlic powder, and onion powder until combined.
Add the shredded chicken to the sauce and toss until the chicken is evenly coated.
Arrange the flatbreads on a baking sheet. Drizzle each with a little olive oil and a spoonful of the hot sauce mixture, spreading it evenly over the surface.
Top each flatbread with sliced mozzarella, distributing the cheese but leaving some space in the center for the chicken.
Place the sauced shredded chicken around the mozzarella (not directly on top of every slice) and season with salt and pepper.
Broil the flatbreads for about 5 minutes, or until the cheese has melted and edges are lightly browned; watch closely to avoid burning.
While the flatbreads broil, chop the avocado and finely chop the red onion.
Remove the flatbreads from the oven. Drizzle with Greek yogurt, then top with chopped avocado, red onion, and pea shoots or arugula. Serve immediately.