Marinate the chicken: In a bowl, whisk olive oil, lemon juice and zest, garlic, oregano, cumin, salt, pepper, and red pepper flakes. Add chicken and toss to coat.
Cover and refrigerate at least 30 minutes, up to 8 hours.
Make the tzatziki: Grate the cucumber, then squeeze out excess water with a clean towel. Stir yogurt, cucumber, olive oil, lemon juice, garlic, dill, salt, and pepper. Adjust salt and lemon to taste.
Chill until serving.
Prep your base and toppings: Cook rice according to package directions. Chop tomatoes, cucumber, onion, and parsley. Pit and slice olives.
Crumble feta.
Cook the chicken: Heat a large skillet or grill pan over medium-high heat. Add a light film of oil. Cook chicken 4–6 minutes per side (thighs) or 4–5 minutes per side (breasts), until browned and cooked through.
Rest 5 minutes, then slice.
Assemble the bowls: Add a scoop of rice to each bowl. Top with sliced chicken, tomatoes, cucumber, red onion, olives, and feta. Add a generous dollop of tzatziki.
Finish and serve: Sprinkle with parsley, add a squeeze of lemon, and, if you like, a light drizzle of olive oil and a splash of red wine vinegar.
Serve warm with extra tzatziki.