Place an oven rack in the second-highest position and heat broiler.
Combine the lamb, raisins, cinnamon, 1 1/2 teaspoons salt, 1/4 teaspoon pepper, the bread crumbs, egg, and three-quarters of the scallions in a large bowl.
Shape the mixture into golf ball–size meatballs and place on a foil-lined baking sheet.
Broil, turning once, until cooked through, 6 to 8 minutes total.
Divide the flat bread among individual plates and top with the meatballs, yogurt, mint, and the remaining scallions.