Place flour in a shallow bowl; season generously with salt and pepper. Dredge each piece of chicken in flour, shaking off excess.
In a large skillet, heat oil over medium. Add chicken, and cook until golden on the outside and opaque throughout, 8 to 10 minutes per side. Transfer to a plate, and cover with aluminum foil to keep warm (reserve skillet).
Add mushrooms, shallot, sage, and 1/4 cup water to skillet; season with salt and pepper. Cook, tossing frequently, until mushrooms are tender, 3 to 5 minutes. Add wine and cream; simmer over medium-high until slightly thickened, 3 to 5 minutes. Remove from heat, and stir in butter; season with salt and pepper.
Top chicken with mushroom sauce, and garnish with sage.