In a large bowl, whisk together olive oil, red wine vinegar, lemon juice, minced garlic, oregano, salt, black pepper, and red pepper flakes to create a marinade.
Add the chicken thighs to the marinade, ensuring they are fully coated. Cover and refrigerate for at least 30 minutes, or up to 2 hours for more flavor.
Preheat your grill to medium-high heat. Remove the chicken from the marinade and discard the marinade.
Grill the chicken for about 6-7 minutes on each side, or until the internal temperature reaches 165°F and the chicken is nicely charred.
While the chicken is grilling, prepare the salmoriglio sauce by mixing together the chopped parsley, basil, and a drizzle of olive oil in a small bowl.
Once the chicken is cooked, remove it from the grill and let it rest for 5 minutes. Serve topped with the salmoriglio sauce and lemon slices.