Whisk tamari, maple syrup, ginger, and garlic together in a large bowl; add chicken and toss to coat. Whisk chicken broth, flour, fish oil, and lime juice together in another bowl.
Place noodles in a large bowl and cover with hot water. Set aside until noodles are softened, 10 to 15 minutes. Drain and rinse thoroughly.
Heat coconut oil in a large skillet or wok over medium-high heat. Cook and stir chicken in hot oil until golden all over, about 5 minutes. Pour chicken broth mixture over chicken and bring to a boil; stir mushrooms, green onion, red bell pepper, and red chile pepper into chicken mixture, cover the skillet with a lid, reduce heat to medium-low, and cook until vegetables are slightly tender, about 5 minutes.
Stir bean sprouts, cilantro, and noodles into chicken mixture; cook and stir until all ingredients are heated through, 3 to 5 minutes.