Cut chicken thighs into 1-inch pieces, aiming for uniform sizes.
In a large mixing bowl, whisk together Greek yogurt, olive oil, and vinegar until smooth and creamy.
Add chopped garlic, oregano, turmeric, salt, and red pepper flakes (if using). Whisk thoroughly until spices are evenly distributed.
Add chicken pieces to the marinade and toss until every piece is coated. Cover the bowl with plastic wrap and refrigerate for at least 1 hour, up to 8 hours.
If using wooden skewers, soak them in water for 30 minutes. Preheat grill or grill pan to medium-low heat.
Thread marinated chicken onto 4 skewers, leaving small gaps between pieces. Discard leftover marinade. Season both sides with salt and freshly cracked black pepper.
Place skewers on preheated grill and cook for about 15 minutes total, turning occasionally, until chicken reaches 165°F internal temperature and has golden brown char marks.
While chicken grills, make the fresh salad. In a medium bowl, whisk together olive oil and vinegar. Season with salt and pepper.
Add sliced cucumbers, halved tomatoes, and sliced red onion to the dressing. Toss gently to coat. Taste and adjust seasoning as needed.
Divide cooked quinoa among 4 bowls (about 1/2 cup per bowl). Fluff gently with a fork.
Spoon fresh cucumber salad over one section of the quinoa. Add a generous dollop of tzatziki sauce (about 1/4 cup per bowl).
Sprinkle 1 tablespoon crumbled feta over each bowl and add 3 smashed Castelvetrano olives.
Top each bowl with one chicken skewer. Serve immediately while chicken is still warm.