Pat the chicken thighs dry with paper towels and place them in a large zip-top bag or shallow dish.
Add the olive oil, lemon juice, red wine vinegar, garlic, smoked paprika, oregano, salt, black pepper, cayenne, and optional red pepper flakes to a blender or small food processor. Blend until mostly smooth. Alternatively, finely mince the garlic and whisk everything together in a bowl.
Set aside 1/4 cup (60 ml) of the clean marinade for serving later. Pour the remaining marinade over the chicken, turning the pieces to coat. Cover and refrigerate for at least 30 minutes or up to 8 hours.
Preheat a gas grill for two-zone cooking, with one side on medium heat and one side off, aiming for about 375°F (190°C). For a charcoal grill, bank the coals on one side to create direct and indirect zones. Clean and oil the grates.
Remove the chicken from the marinade, letting excess drip off. Discard the used marinade. Place the thighs skin-side up on the indirect-heat side of the grill. Close the lid and cook for 20 to 25 minutes, turning once halfway through.
Move the chicken skin-side down over direct medium heat. Grill for 2 to 4 minutes per side, watching closely, until the skin is browned with light char marks and an instant-read thermometer inserted into the thickest part, not touching bone, reads 165°F (74°C).
Transfer the chicken to a clean platter and rest for 5 minutes. Spoon or brush the reserved clean marinade over the chicken, then garnish with parsley and serve with lemon wedges if desired.