Bring a large pot of salted water to a boil and cook the whole wheat spaghetti according to package directions until al dente.
While the pasta cooks, slice the chicken breast into bite-sized strips and chop the broccoli, bell pepper, and snap peas.
Heat the toasted sesame oil in a large wok or skillet over medium-high heat.
Add the chicken strips to the skillet and sauté until golden brown and cooked through, about 5-7 minutes.
Stir in the minced garlic, grated ginger, and red pepper flakes, cooking for 1 minute until fragrant.
Add the broccoli, red bell pepper, and snap peas to the pan, stir-frying for 3-4 minutes until they are vibrant and crisp-tender.
Drain the spaghetti and add it to the skillet along with the tamari and rice vinegar.
Toss everything together for 2 minutes over heat to ensure the noodles are well-coated and the flavors are combined.
Garnish with sliced green onions before serving.