In a large Dutch oven, crisp the bacon over medium heat and transfer to a paper-towel-lined plate. If there's too much fat left in the pot, pour some out (reserve it!), leaving enough to brown the chicken.
Place flour on a platter. Season the chicken pieces with salt and pepper, then dredge them in the flour. Working in batches so as not to crowd the pot, brown the chicken over medium heat until deep golden brown and crisp, 12-15 minutes. Transfer to a plate.
Add more bacon fat if needed, then add the chopped onion. Cook until it is translucent, 5-8 minutes. Add the garlic and mushrooms and cook until the mushrooms are browned and have released most of their liquid.
Add the white wine to deglaze the pan and reduce it by half, 3-5 minutes. Season with salt and pepper.
Add the bacon and chicken back to the pot, then add the thyme, bay leaves, and broth. Bring to a boil, reduce the heat, and gently simmer, partially covered, until the chicken is falling off the bone, 2-2½ hours.