Preheat your oven to 425°F. Line a baking sheet with parchment paper.
Lay the flatbreads on the prepared baking sheet. Brush each one generously with olive oil.
Top each flatbread with torn mozzarella, then scatter the shredded rotisserie chicken evenly over both. Sprinkle with Parmesan and a pinch of flaky salt and fresh cracked pepper.
Bake for 10–12 minutes, until the cheese is melted and bubbly and the edges of the flatbread are golden and crisp.
While the flatbreads bake, toss the arugula in a small bowl with olive oil, lemon juice, and a pinch of flaky salt.
Remove flatbreads from the oven. Pile the arugula salad on top of each flatbread. Finish with a generous amount of lemon zest and an extra shower of grated Parmesan.
Slice and serve immediately — the arugula wilts slightly from the heat of the flatbread, which is exactly what you want.