Preheat your oven to 425°F. While it heats, prepare all your toppings: halve the cherry tomatoes, thinly slice the red onion, pit and halve the Kalamata olives, and crumble the feta cheese. Having everything ready before you start assembling makes the process quick and ensures even cooking. Place your flatbreads on a baking sheet and set aside.
Spread about 2-3 tablespoons of pesto evenly on each flatbread, leaving a small border around the edges. Sprinkle the shredded mozzarella cheese over the pesto on both flatbreads—this creates a melting layer that helps bind everything together. I like to use slightly less mozzarella than you'd think because the feta adds plenty of saltiness later.
Distribute the shredded chicken evenly over the mozzarella on both flatbreads. Then add your fresh toppings in this order: scatter the spinach first (it wilts slightly during baking), followed by the cherry tomatoes, red onion slices, and Kalamata olives. This layering order ensures the spinach nestles into the warm cheese while delicate toppings stay on top where they won't get buried.
Sprinkle the crumbled feta cheese over the top of both flatbreads, distributing it evenly. Lightly drizzle a small amount of pesto over each pizza (about 1-2 teaspoons total per flatbread), and finish with a light dusting of garlic powder across both. I find the extra pesto drizzle brings the Mediterranean flavors together without overpowering the dish.
Transfer the baking sheet to your preheated 425°F oven and bake for 10-12 minutes, until the edges of the flatbreads are golden and crispy and the mozzarella is melted and slightly bubbling. The flatbread should have a light char in spots for the best texture. Remove from the oven, let cool for 1-2 minutes, cut each flatbread in half or into serving pieces, and serve immediately while still warm.