In a saucepan, cover the chickpeas with 2 inches of water and bring to a boil. Simmer over low heat until the chickpeas are tender, about 1 hour; add more water as needed to keep them covered. Reserve 1/4 cup of the cooking liquid and drain the chickpeas. Transfer the chickpeas to a food processor. Add the reserved cooking liquid and the remaining hummus ingredients and process until smooth. Season with salt.
In a large bowl, whisk the flour, salt and baking powder. Stir in the water and olive oil and knead to form a moist dough. Cover with a kitchen towel and let rest for 30 minutes.
Heat a 10-inch cast-iron skillet. Divide the dough into 16 balls. On a lightly floured work surface, roll out each ball to a 6-by-3-inch oval. Cook 2 flatbreads at a time in the skillet over moderate heat until they start to brown on the bottom, about 2 minutes. Flip and cook until browned in spots on the other side, about 2 minutes. Just before serving, turn each flatbread over an open flame until lightly charred, 1 minute. Serve with the hummus.