Rinse tomatoes and cut into wedges. Rinse, halve lengthwise and julienne zucchini and cucumber. Peel onions, halve lengthwise and cut crosswise into strips. Add cut vegetables and black olives to a bowl.
Stir together olive oil, white wine vinegar and sugar to make salad dressing. Rinse parsley, chop and shake dry. Mix half parsley into salad dressing and season with salt and pepper. Mix dressing with salad.
For the dip: Stir together quark and mineral water until smooth. Peel and press garlic. Rinse chives, shake dry and cut into small rings. Mix chives, garlic and remaining parsley with quark and season with salt and pepper.
Just before serving warm small flatbreads on grill, turning once. Serve flatbread with cucumber salad and dip.