In a medium bowl, whisk together olive oil, lemon juice, minced garlic, oregano, salt, and pepper.
Add cubed chicken to the marinade and toss to coat.
Heat a skillet or grill pan over medium-high heat and cook chicken until internal temperature reaches 165 degrees Fahrenheit, approximately 8 to 10 minutes.
Warm the flatbreads in a low oven or on the grill for 1 to 2 minutes until soft and pliable.
Spread a layer of tzatziki sauce over the surface of each flatbread.
Distribute the cooked chicken, tomatoes, cucumber, red onion, and olives evenly across the flatbreads.
Top with crumbled feta cheese and fresh parsley before serving.