In a medium bowl, mix together the olive oil, lemon juice, smoked paprika, cumin, garlic, turmeric, coriander, salt, pepper, onion powder, cinnamon, and red pepper flakes. Add the chicken breast and coat evenly. Let it marinate for 20 minutes.
Prep all ingredients per the instructions above.
To make the tzatziki sauce, combine garlic, cucumber, dill, Greek yogurt, lemon juice, salt, and pepper in a blender. Blend until smooth. Taste and adjust seasoning if needed. Refrigerate until ready to use.
Heat a grill pan or griddle over medium heat.
Remove the chicken from the marinade and let excess liquid drip off. Grill on each side to an internal temperature of 165°F / 74°C. Transfer the chicken to a plate and let it rest for a few minutes before slicing into bite-sized pieces.
Warm the pita bread for about 30 seconds on each side in the grill pan until soft and slightly toasted.
Assemble each gyro by layering romaine lettuce, grilled chicken, red onion, grape tomatoes, kalamata olives, feta cheese, and a generous spoonful of tzatziki sauce inside the warm pita.
Make the peach ginger chia fresca: combine all the ingredients together. Let sit for 5 minutes to allow the chia seeds to expand, then stir again.
Serve the gyro alongside carrots, hummus, and peach ginger chia fresca.