Mince the garlic and finely chop the parsley, cucumber, tomatoes, and red onion.
In a small bowl, whisk together the Greek yogurt, half of the lemon juice, and half of the minced garlic to create the sauce.
Season the chicken breast with the remaining lemon juice, garlic, dried oregano, sea salt, and black pepper.
Heat the olive oil in a skillet over medium-high heat and sear the chicken for 5-7 minutes per side until golden brown and cooked through.
Remove the chicken from the pan, let it rest for 3 minutes, then slice into thin strips.
Place the flatbread in the same skillet for 1 minute per side until it becomes warm and slightly crispy.
Spread the yogurt sauce over the flatbread, then layer with the sliced chicken, cucumber, tomatoes, red onion, parsley, and crumbled feta.
Fold the flatbread in half and serve immediately while the chicken is hot and the bread is crunchy.