In a bowl, combine parsley, cilantro, garlic, olive oil, red wine vinegar, lemon juice, oregano, red pepper flakes, salt, and pepper. Mix well to create the chimichurri sauce. Reserve half of the chimichurri sauce for serving and use the rest as a marinade. Place the chicken breasts in a resealable plastic bag or shallow dish, pour the marinade over them, and let them marinate in the refrigerator for at least 30 minutes or up to 2 hours. Preheat your grill to medium-high heat. Remove the chicken from the marinade, letting any excess drip off, and grill for 6-7 minutes per side, or until the internal temperature reaches 165°F (75°C). Transfer the grilled chicken to a serving plate and let it rest for 5 minutes. Drizzle with the reserved chimichurri sauce and serve with your favorite sides like rice, roasted vegetables, or salad.