Place a baking sheet in the oven and preheat to 250 degrees .
In a medium skillet, heat the oil, one turn of the pan, over medium-high. Add the onion, chile and garlic. Season with salt and pepper. Cook, stirring often, until softened, 3 to 4 minutes. Add the tomato; toss 1 minute. Add the beans, chipotle in adobo and cinnamon; season. Off heat, stir in the cilantro.
Heat a small nonstick skillet over medium-high. Add a dab of butter. When the butter melts, add a tortilla; cook until golden, 30 to 60 seconds. Lightly beat 1 egg. Pour the egg over the tortilla; season with salt and pepper. Quickly flip the tortilla so the egg is on the bottom. Cook until the egg browns, 30 to 60 seconds. Flip the tortilla over; scatter with about 1/4 cup cheese. Spoon a few tablespoons of beans along one edge. Starting at the edge with the beans, roll up the tortilla. Transfer to the baking sheet in the oven. Repeat with the remaining butter, tortillas, eggs, cheese and beans.
Line plates with the lettuce. Top each with 2 flautas. Dress the avocado slices with the lime juice; place on top of the flautas. Serve the flautas with the hot sauce.