Place the chicken breasts between sheets of plastic wrap and gently pound them to about ½-inch thickness. Add the chicken to a bowl or zip-top bag.
Whisk together the olive oil, lemon juice, lemon zest, white wine vinegar, oregano, garlic powder, thyme, basil, salt, black pepper, and red pepper flakes. Pour the marinade over the chicken and turn to coat. Refrigerate for at least 30 minutes or up to several hours.
While the chicken marinates, make the tzatziki. Stir together the Greek yogurt, grated cucumber, lemon juice, olive oil, garlic, dill, and salt. Refrigerate until ready to use.
Prepare the rice or quinoa and chop the cucumber, tomatoes, red onion, and romaine. If using olives, slice them in half.
For skillet cooking, heat a lightly oiled skillet over medium heat. Cook the chicken for about 7–8 minutes on the first side, then flip and cook until browned and the center reaches 165°F.
For air-fryer cooking, preheat the air fryer to 380°F. Cook the chicken for about 7 minutes, flip, then cook for another 3–4 minutes or until it reaches 165°F.
Let the cooked chicken rest for about 5 minutes, then slice it into strips.
Divide the rice or quinoa and romaine among four bowls. Add the cucumber, tomatoes, red onion, feta, and Kalamata olives.
Top each bowl with sliced Greek chicken and a spoonful of tzatziki. Finish with a squeeze of fresh lemon and an optional drizzle of olive oil.