Zest and juice half the lemon. Peel and grate or crush the garlic. Add both to a large bowl with 2 tsp sumach and ½ tbsp oil. Season. Mix together. Peel and thickly slice the onions and add to the bowl. Tip in the chicken and turn to coat in the marinade. Set aside for 10 mins to marinate.
Spoon 2 tbsp of yogurt into a large bowl. Add 1 tbsp oil and 3 tbsp cold water. Whisk together with a pinch of salt. Tip in the flour and stir with a fork to make a soft dough. Turn out onto your work surface and knead for 2-3 mins to form a smooth dough. Pop back in the bowl, cover with a tea towel and leave to rest.
Using a vegetable peeler, peel long ribbons off the courgette. Turn and peel down to the seeded core, which you can discard. Set the courgette ribbons aside.
Heat the grill to its highest setting. Line a baking tray with foil. Tip the sumach chicken and onions onto the tray. Grill for 8-10 mins, turning the chicken halfway through the cooking time, till it is charred and cooked all the way through.
While the chicken cooks, divide the dough into 2 balls and roll each one out into a large circle. Brush 1 tsp oil on each side of the flatbreads. Heat a frying or griddle pan over a medium heat.
When the pan is hot, lay a flatbread in the pan and cook for 2 mins on each side till browned and puffed up. Slide the cooked flatbread onto a plate and cover with a tea towel to keep warm while you cook the remaining flatbread.
Lay each flatbread on a plate. Top with the courgette ribbons. Spoon over the hot sumach chicken and onions, drizzling over any juices from the tray. Scatter over the parsley leaves and serve with the remaining yogurt and wedges of the remaining lemon for squeezing.