In a medium bowl, combine the chicken pieces with olive oil, lemon juice, minced garlic, oregano, salt, and pepper. Stir to coat and set aside to marinate for at least 10 minutes.

While the chicken marinates, prepare the tzatziki. Grate the cucumber and squeeze out all excess liquid. In a small bowl, mix the squeezed cucumber, Greek yogurt, fresh dill, and lemon juice. Season with a pinch of salt. Set aside.

Heat a large skillet over medium-high heat. Add the marinated chicken and cook, stirring occasionally, for 6-8 minutes, or until golden brown and cooked through.

Warm the flatbreads in a dry skillet or oven until soft and slightly toasted.

To assemble, spread a layer of tzatziki sauce on each warm flatbread. Top with the cooked chicken, tomatoes, red onion, feta cheese, and Kalamata olives. Serve immediately.