In a large skillet or Dutch oven, fry the bacon in the olive oil over medium heat until brown and crisp. Using a slotted spoon, transfer the bacon to a paper-towel-lined plate. Add the chicken to the pan, skin side down, and fry, turning once, until golden brown on both sides, about 10 minutes. Transfer the chicken to the plate with the bacon.
Add the mushroom stems and garlic to the pan and cook until softened, about 2 minutes. Sprinkle the flour over everything in the pan. Stirring with a whisk, cook through, 1 to 3 minutes. Whisk in the wine and chicken broth until combined. Season with a pinch of salt and pepper and the thyme; bring to a boil. Lower the heat, return the chicken and bacon to the pan, cover and simmer for 40 minutes.
Stir in the mushroom caps and cook until softened, about 5 minutes. Transfer the chicken to a plate, discard the skin and return the chicken to the pan; stir to coat. Season with salt and pepper. Serve over the pasta.