For the quick pickled onions, combine the vinegar, water, sugar, and salt in a small microwave-safe bowl and heat until the sugar and salt mostly dissolve, about a minute or so. Add the onions, turning them to coat in the mixture. Set aside.
For the tzatziki, lightly squeeze any excess water out of the cucumber over the sink (with your hands or with the cucumber wrapped up in a towel). In a bowl, stir together the yogurt, lemon juice, garlic, and a pinch of salt and pepper. Add the drained cucumber, and stir to combine. Drizzle with a teaspoon or so of olive oil. Set aside.
For the chicken, in a small bowl, stir together the oregano, basil, onion powder, garlic powder, salt and pepper.
Pat the chicken pieces dry and rub the spice mixture all over both sides of the chicken.
Preheat a grill (or grill pan, broiler or skillet) to medium-high. Grill/cook the chicken for 4-5 minutes per side (exact time will depend on the thickness of the chicken) until cooked through; an instant-read thermometer should register 165 degrees F.
Lightly tent the chicken with foil and let rest for 5-10 minutes.
To assemble, heat the flatbread/wraps/tortillas until just warm (in a skillet or I sometimes throw them into a ziploc bag and microwave with the bag opened for 30-45 seconds).
Cut the chicken into cubes or slices. Arrange the chicken down the center of each flatbread. Top with lettuce, tomatoes, pickled onions, tzatziki and feta cheese. Roll up, cut in half, if desired, and serve immediately.
