To make the marinade, mix the lemon juice, oil, vinegar, chile flakes, oregano, garlic and sprinkle with salt and pepper in a small bowl. In a plastic bag or airtight container, add the chicken pieces, potatoes, carrots and onions. Add the marinade to bag, toss well to coat evenly, and refrigerate 1 to 10 hours.
Preheat the oven to 400 degrees F.
Place the potatoes, carrots and onions in a single layer in a large glass baking dish. Transfer the chicken and place on top of the vegetables. Drizzle all the marinade from the bag over the chicken. Roast the chicken until it's cooked through, or an instant-read thermometer registers 165 degrees F, about 40 minutes. Cover the chicken and let rest for 5 minutes before serving.