Pat the chicken dry with paper towels and cut it into 1-1/2-inch pieces. Place in a large bowl, add the measured salt and pepper, and toss to combine. Add the flour and toss to coat.
Heat 1 tablespoon of the oil in a Dutch oven or a large, heavy-bottomed pot (at least 6 1/2 quarts) over medium heat until shimmering. Add a third of the chicken in a single layer, shaking any excess flour into the bowl first. Sear until golden brown on both sides, about 10 minutes. Transfer to a large heatproof bowl. Repeat with the remaining chicken in two more batches, using a tablespoon of oil for each batch.
Heat 1 tablespoon of the oil over medium heat in the same pot until shimmering. Add the onion and garlic and cook, stirring occasionally, until soft, about 5 minutes. Transfer the mixture to the bowl with the chicken.
Heat the remaining 1 tablespoon oil in the same pot over medium heat until shimmering. Add the Anaheim chiles, poblanos, Aleppo pepper, cumin, and paprika and cook, stirring occasionally, until the peppers are tender, about 4 minutes.
Add the reserved chicken-onion mixture, tomatillos, chicken broth, potatoes, oregano, and cinnamon stick to the pot and stir to combine. Bring to a boil over high heat, then reduce the heat to medium low and simmer, stirring occasionally, until the mixture thickens and the potatoes are tender, about 1 1/2 hours.
Stir in the cilantro, taste, and season with salt as needed.
Beverage pairing: With its combination of earthy vegetables and assertive spices, this dish calls for something a little exotic like the 2005 The FMC, an off-dry Chenin Blanc from South African master of the grape Ken Forrester. Complex with herbs, earth, fruit, and toast, the lightly oaked wine is a touch sweet, which will soothe any spiciness in the chile verde.