Marinate the Chicken: In a medium bowl, mix the diced chicken breast with the other marinade ingredients and refrigerate for at least 20 minutes.
Make Tzatziki: Grate the cucumber using the large side of a box grater and squeeze out the liquid. In a bowl, combine the yoghurt, dry cucumber, mint, and garlic. Add lemon juice and stir until combined. Season to taste.
Build the Chicken: Preheat an overhead grill. While the grill heats up, remove the chicken from the fridge and begin skewering the meat onto long metal skewers. This recipe should yield eight skewers.
Cook the Chicken: Place the skewered chicken onto a grill tray lined with kitchen foil, and place it under the hot grill. Grill the chicken for 16-20 minutes, or until it is cooked through. Turn the skewers at least once to brown on all sides.
Build: Lightly toast the flatbread on the same tray as the chicken, then serve it loaded with diced vegetables and a generous dollop of tzatziki.