Prepare flatbread dough and allow to rise.
Season lamb with salt and cumin. Brown in olive oil in a Dutch oven. Remove and set aside.
Add onion and garlic to the drippings and cook until softened.
Return lamb to the pot. Add red wine and water until partially submerged.
Cover and braise gently for 1–2 hours until tender.
When lamb is nearly done, bake flatbread at 400°F until cooked and lightly browned.
Remove lamb and shred.
Add pomegranate juice to the braising liquid and whisk in a small amount of flour, stirring aggressively until thickened.
Combine herbs, onions, nuts, and olive oil to make the slaw.
Assemble flatbread with shredded lamb, herb slaw, and pomegranate sauce.