Mash the avocados with the lime juice in a medium bowl. Season with about 1 tsp. of the salt and the pepper, or to taste.
Set a large, heavy-based skillet over medium heat. Add the oil and onion, sprinkle with the remaining 1/2 tsp. salt, and cook, stirring, until softened and translucent, about 6 minutes. Add the chili powder and cinnamon and cook, stirring, for 30 seconds. Add the tomatoes, chipotle, and adobo sauce and cook, stirring, for 5 minutes, mashing the tomatoes with a wooden spoon. Stir in the chicken, cover, reduce the heat to low, and cook until the chicken heats through, about 10 minutes. Taste, and season with salt and pepper if needed.
Let diners assemble their own tacos by spreading the warm tortillas with the avocado and then topping with the chicken, cheese, cabbage, cilantro, and a squeeze of juice from the lime wedges.