Bring a large saucepan of water to a boil. Cook noodles according to package directions.
While noodles are cooking, in a medium bowl, combine chicken with scallion whites, garlic, ginger, and pepper flakes; season lightly with salt.
Drain noodles and transfer to another medium bowl. Add scallion greens, soy sauce, and sesame oil.; toss to combine. Season lightly with salt.
In a large nonstick skillet or wok, heat vegetable oil over medium-high heat. Add chicken, and cook, stirring constantly, until just cooked through, 4-5 minutes. Transfer chicken to a plate.
Return the pan to the heat. Add cabbage, mushrooms, and water. Cook, stirring until vegetables are wilted, about 4 minutes. Return chicken and noodles to the pan, stir, and cook to heat through, about 1 minute. Toss with lemon juice and serve warm.