For tzatziki, in a small bowl combine cucumber, yogurt, lemon juice, 1 teaspoon dill, garlic, and salt. Fold in 1/4 cup cheese. If desired, cover and chill for up to 2 hours.
On four 10- to 12-inch skewers* alternately thread zucchini, yellow squash, mushrooms, and onion, leaving 1/4 inch between pieces. Brush with oil; sprinkle with oregano and crushed red pepper.
For a charcoal or gas grill, place skewers on the rack of a covered grill directly over medium heat. Grill for 12 to 14 minutes or until vegetables are tender, turning occasionally. Remove from grill. Place pita flatbreads on grill rack. Grill for 2 to 4 minutes or until heated through and lightly toasted, turning once halfway through grilling.
Spread pita flatbreads with tzatziki. Folding a flatbread around each skewer, hold the vegetables with the bread while pulling out the skewer. Top with tomato slices and, if desired, additional dill and/or cheese. Fold in half.
If using wooden skewers, soak in water for at least 30 minutes; drain before using.