Add the minced garlic, apple cider vinegar, lemon juice, olive oil, Greek yogurt, dried oregano, salt, and black pepper to a large food-safe bag or covered container. Mix thoroughly.
Add the chicken thighs and turn or massage them gently until every piece is evenly coated with marinade. Refrigerate for at least 2 hours, preferably 3–12 hours. Do not marinate for longer than 24 hours.
To make the tzatziki, cut the cucumbers lengthwise and scoop out the watery seeds with a teaspoon. Coarsely grate the cucumber.
Place the grated cucumber in a clean kitchen towel or several layers of paper towels. Squeeze firmly to remove as much excess moisture as possible.
Transfer the cucumber to a bowl. Add Greek yogurt, lemon juice, olive oil, minced garlic, salt, and black pepper. Stir until combined and refrigerate for at least 20 minutes so the flavors can develop.
Prepare the salad by combining diced tomatoes, cucumbers, red onion, and optional parsley in a bowl. Season lightly with salt and black pepper.
Preheat an outdoor grill to medium-high and lightly oil the grates. Alternatively, heat a small amount of oil in a large skillet over medium-high heat.
Remove the chicken from the marinade and discard the remaining marinade. Cook the chicken until browned on both sides and completely cooked through. Because thigh thickness varies, check the thickest piece with a food thermometer; chicken should reach 165°F (74°C).
Transfer the cooked chicken to a clean plate and rest for about 5 minutes. Slice larger thighs into strips or bite-sized pieces.
Warm the pita or flatbreads until soft and flexible.
Assemble the Greek Chicken Gyros by placing salad along the center of each pita. Add warm chicken and a generous spoonful of tzatziki.
Fold or roll the pita around the filling and serve immediately.