With your hands, flatten bread dough on a board. Top with olive oil and green onions and knead into dough until incorporated (dough will be sticky).
Place dough in a bowl and cover. Let rise in a warm place until doubled, 50 to 60 minutes.
On a floured board, knead dough briefly to expel air. Divide into 12 equal pieces. Shape each into a ball and coat with flour. Roll each ball into a 4- to 5-inch round, sprinkling with flour as needed to prevent sticking. Space rounds evenly on two floured 15- by 17-inch baking sheets. Cover loosely and let rise until puffy, 20 to 30 minutes.
Lay rounds of dough on a lightly oiled barbecue grill over a solid bed of medium coals or medium heat on a gas grill (you can hold your hand at grill level only 4 to 5 seconds); close lid (open vents for charcoal). Cook until rounds are browned on the bottom, about 2 minutes; turn, replace lid, and cook until browned on the other side, 1 to 2 minutes longer.
Transfer breads to a bowl. Serve hot (cover with foil to keep warm up to 30 minutes) or cool.
Note: Nutritional analysis is per flatbread.