Preheat the oven to 400 degrees. (Preheat a pizza stone if you have one, otherwise preheat a baking sheet)
Add the ingredients for the flatbread into food processor and pulse until smooth. Scrape down the sides as needed and pulse until everything is combined. Taste and season with salt and pepper. Adjust any of the other ingredients as needed to taste.
Place the mixture onto a piece of parchment paper and form into a round flat disc. (Make more than one if needed depending upon the amount of mixture you have).
Place on the preheated pizza stone or baking sheet. Cook until the bottom turns golden brown, about 10 minutes. Then remove from the oven, place another piece of parchment paper over top and carefully invert the flatbread. Place the uncooked side on the stone or pan and cook until golden brown. Remove from the oven and set aside to cool. (If the flatbread starts to come apart while inverting just press it back together with your hands so its tightly compacted). In the meantime, heat a nonstick pan on medium heat. Once hot, add the oil. Brown the chicken on both sides to deep golden brown. Place in the oven and cook to an internal temperature of 160 degrees using a thermometer. Set aside to rest. Chopped before serving.
Whisk together all the ingredients for the sauce. Season with salt. Adjust any of the ingredients to taste.
For the salad: In a bowl whisk together the oil, mustard, vinegar, oregano, and garlic until fully combined. Toss the spring mix with onion and carrot. Dress right before serving.
Spread the yogurt sauce onto the flatbread. Top with cucumber, tomato, chicken, and feta. Drizzle with olive oil. Cut into wedges.
Serve with salad. Garnish with cilantro.