Pat chicken breasts dry with paper towels. If breasts are unevenly thick, place between plastic wrap and gently pound the thicker sections to achieve uniform thickness of approximately 3/4 inch (1.9 cm).
In a glass or non-reactive bowl, combine yogurt, olive oil, garlic, lemon zest, lemon juice, salt, pepper, oregano, cumin, paprika, and red pepper flakes if using. Whisk until completely homogeneous.
Place chicken breasts in the marinade, ensuring complete coverage on all surfaces. For optimal penetration, make shallow scores (1/8 inch deep) in a crosshatch pattern on the thickest parts of the breasts before marinating.
Cover and refrigerate for 4-8 hours (minimum 2 hours, maximum 24 hours).
Remove marinated chicken from refrigerator 30 minutes before cooking to allow it to approach room temperature.
Preheat oven to 425°F (218°C) and allow full preheating cycle to complete.
Line a rimmed baking sheet with parchment paper and place a wire rack on the sheet. Remove chicken from marinade, gently wiping off excess while leaving a thin coating. Position chicken on the wire rack with at least 1 inch (2.5 cm) between pieces.
Place in center rack of oven and bake until internal temperature reaches 163°F (72.8°C) at the thickest point, approximately 18-22 minutes depending on thickness.
Remove from oven and allow to rest for 5-7 minutes, during which carryover cooking will bring the temperature to the food-safe 165°F (73.9°C) while allowing muscle fibers to reabsorb moisture.
Slice against the grain or serve whole as desired.