In a large nonstick pot or pan, heat the olive oil. Add mushrooms, garlic, ginger and cook over medium heat for about 4 minutes. Stir often. Mix in broth, vinegar, soy sauce, and red pepper flakes. Bring to a boil. Stir in broccoli slaw or cabbage and chicken. Return to a boil; reduce heat and simmer, uncovered, for 5 minutes.