Score the skin side of each chicken breast several times and place in a bowl. Add the pomegranate molasses, oil, zumac and a generous sprinkling of salt and pepper. Rub into the chicken and leave to marinate in a cool place for 1 hour.
Remove the chicken from the marinade, reserving the juices, and cook on a medium-hot barbecue for 6—8 minutes on each side until charred and cooked through. Set aside to rest for 5 minutes.
Heat the reserved marinade juices in a small pan until boiling and reduced slightly. Brush over the cooked chicken to glaze.
Meanwhile, make the salad. Cut the aubergine crossways into 5 mm (¼ inch) thick slices. Brush with a little of the oil and cook on a hot barbecue for 1–2 minutes each side. Toast the flatbreads on the barbecue for 30 seconds or so on each side until crisp, then crumble into a large bowl. Add the tomatoes, cucumber, olives, herbs and pomegranate seeds. Whisk the remaining oil, lemon juice, sugar and a little salt and pepper and add to the salad. Toss well and serve with the chicken.