In a large pot of boiling water, cook lo mein egg noodles according to package instructions; drain well.
Whisk together soy sauce, honey, rice vinegar, sesame oil, ginger, and Sriracha sauce and set aside.
Heat 1 tsp olive oil in a large, nonstick skillet over medium-high heat. Cook chicken pieces until browned on both sides, and no longer pink in the middle, about 4-6 minutes. Remove chicken and set aside.
Add remaining tsp olive oil, add in broccoli slaw and garlic, and cook, stirring frequently, until tender, about 3-4 minutes. Stir in snow peas and spinach until the spinach has wilted, about 2-3 minutes.
Stir in the lo mein noodles, chicken, and soy sauce mixture, and toss gently to combine. Serve immediately.