Heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the chicken pieces, season with salt and pepper, and cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the remaining 2 tablespoons of olive oil. Add the minced garlic and sauté for about 30 seconds until fragrant.
Add the sliced red bell pepper and snap peas to the skillet. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Return the cooked chicken to the skillet. Pour in the soy sauce and sesame oil, and add the crushed red pepper flakes if using. Stir to combine and heat through for another 2 minutes.
Add the spiralized zucchini noodles to the skillet. Toss everything together and cook for an additional 2-3 minutes until the zucchini noodles are just tender but not mushy.
Remove from heat and garnish with chopped green onions before serving.