In a small bowl, whisk together parsley, cilantro, minced garlic, oregano, red pepper flakes, olive oil, and vinegar to create the chimichurri.
Toss chicken thighs with half of the chimichurri mixture and marinate for at least 15 minutes.
Preheat a grill or grill pan to medium-high heat and cook chicken for 6-7 minutes per side until the internal temperature reaches 165°F (74°C).
While chicken cooks, whisk together Greek yogurt, lemon juice, and pressed garlic to create the garlic sauce; season with salt.
Slice the grilled chicken into strips.
Divide cooked rice among four bowls.
Top each bowl with grilled chicken, tomatoes, and cucumber.
Drizzle remaining chimichurri over the chicken and finish with a dollop of garlic sauce.