Combine 1/2 teaspoon oil, hoisin, and next 7 ingredients (hoisin through garlic), stirring well with a whisk.
Heat 1/2 teaspoon oil in a large nonstick skillet over medium-high heat. Add chicken; sauté 4 minutes or until done. Add hoisin mixture to pan; cook 1 minute, stirring frequently. Add mushrooms, cabbage, carrot, and zucchini; cook 3 minutes, stirring occasionally.
Warm tortillas according to package directions. Spoon about 1/2 cup chicken mixture down center of each tortilla; roll up.