Preheat your oven to 400°F (200°C).
In a large bowl, combine the shredded chicken, cherry tomatoes, cucumber, red onion, feta cheese, olives, and parsley.
In a small bowl, whisk together the olive oil, lemon juice, oregano, salt, and pepper. Pour the dressing over the chicken mixture and toss to combine.
Place the flatbread on a baking sheet. Spoon the chicken mixture evenly over each piece of flatbread.
Bake in the preheated oven for 10-12 minutes, or until the flatbread is crispy and the edges are golden.
Remove from the oven and let cool for a couple of minutes before slicing into pieces.