Place the flank steak on a cutting board and cover with plastic wrap. Pound with a meat mallet until an even 3/4–1 inch thickness, then cut the steak into four pieces.
In a small bowl, combine the cumin, coriander, smoked paprika, salt, turmeric, garlic powder, cayenne, and cinnamon; mix well to make the dry rub.
Sprinkle the spice mixture over the steak pieces, turning to coat all sides and edges evenly.
In the same small bowl, whisk together the olive oil, lemon zest, and 2 tablespoons lemon juice. Pour over the seasoned steak and turn to coat. Cover and refrigerate to marinate at least 2 hours.
While the beef marinates, chop the tomatoes, cucumbers, red onion, and parsley or mint, then toss together in a bowl and refrigerate.
Preheat a grill or grill pan to medium-high (about 400°F). Grill the marinated steak 4–5 minutes per side for medium-rare, or longer to desired doneness.
Let the steak rest 5 minutes, then slice thinly against the grain into strips.
To assemble, place several strips of beef on a flatbread, top with cucumber-tomato salad and a dollop of tzatziki, and serve with lemon wedges if desired.
