Toss chicken with olive oil, garlic, lemon zest, lemon juice, salt, pepper, oregano, cumin, coriander, and paprika. Marinate for 20 minutes.
Skewer chicken and grill over medium-high heat for 6-8 minutes, turning until charred and cooked through. Rest for 5-10 minutes, then remove from skewers.
Prepare garlic sauce by whisking together mayonnaise, sour cream, garlic, tahini, sriracha, salt, pepper, cayenne, and lemon juice. Keep refrigerated.
Assemble wraps by spreading garlic sauce on flatbread, adding greens, tomato slices, and chicken. Fold to form a wrap, using parchment or foil if desired.
Notes
Soak skewers in water before grilling to prevent burning. Adjust spice levels to taste.