Place an oven rack in the second-highest position and heat broiler.
Combine the lamb, raisins, cinnamon, 1 ½ teaspoons salt, ¼ teaspoon pepper, bread crumbs, egg, and ¾ of the scallions in a large bowl.
Shape into golf ball-size meatballs and place on a foil-lined baking sheet. Broil, turning once, until cooked through, 6 to 8 minutes.
Divide the flat bread among individual plates and top with the meatballs, yogurt, mint, and remaining scallions.