Whisk together Chobani, mustard, garlic, 2 t salt and ½ t black pepper. Add chicken pieces and turn to coat in marinade. Cover bowl and refrigerate for at least 30 minutes, up to 12 hours.
Preheat oven to 425°F (Gas Mark 7). Line a rimmed baking sheet with foil. Place a wire rack on top of baking sheet and lightly coat with nonstick cooking spray.
Place flour, paprika, thyme, baking powder, remaining 1 t salt and remaining ½ t black pepper in a large plastic bag. Remove chicken from marinade, shake off excess and place in flour mixture. Shake to coat, shake off excess coating and place on prepared rack. Repeat with remaining chicken. Discard remaining marinade and seasoned coating.
Lightly coat chicken with a cooking spray and bake until golden brown and a digital thermometer reads 160°F, 50-60 minutes.