01 - Whisk together olive oil, lemon zest and juice, garlic, oregano, thyme, salt, and pepper. Add chicken breasts, turn to coat evenly. Cover and refrigerate for at least 15 minutes, up to 4 hours for enhanced flavor penetration.
02 - Set oven to 425°F for baking the assembled flatbreads.
03 - Heat a grill pan or skillet over medium-high heat. Remove chicken from marinade and cook for 5 to 6 minutes per side until golden brown and internal temperature reaches 165°F. Transfer to cutting board, let rest for 5 minutes, then slice into thin strips.
04 - Combine Greek yogurt and chopped fresh dill in a small bowl. Mix thoroughly until uniformly blended.
05 - Arrange flatbreads on a large baking sheet. Spread each evenly with dill yogurt mixture. Distribute sliced chicken, cherry tomatoes, red onion, olives, and crumbled feta across both flatbreads.
06 - Place baking sheet in preheated oven and bake for 8 to 10 minutes until flatbread edges become crisp and toppings are thoroughly heated.
07 - Remove flatbreads from oven. Scatter fresh baby arugula over the surface, drizzle with extra virgin olive oil, and season with freshly ground black pepper.
08 - Cut each flatbread into wedges or strips and serve immediately while warm.