Season chicken legs with salt, pepper, and paprika. Warm the canola oil in a heavy frying pan. Add the chicken and cook, turning once, until browned, about 2 minutes per side. Transfer to a plate.
Add mushrooms, bacon, and shallots to frying pan; sprinkle lightly with salt and pepper. Sauté until brown, about 4 minutes. Add garlic; toss for 1 minute. Add thyme, wine, and 1 1/4 cups broth.
Return the chicken to the pan. Cover and reduce heat to medium low. Simmer until the chicken is cooked through, stirring and turning the chicken over occasionally, about 25 minutes.
Whisk flour in small bowl. Add 1/4 cup broth, stirring until smooth.
Add flour mixture to sauce. Cook until sauce thickens, 3 to 4 minutes. Season sauce to taste with salt and pepper.
Divide the chicken amongst 4 warmed plates and serve immediately.