Heat olive oil in a large skillet over medium-high heat until shimmering.
Add garlic and cook for 30 seconds until fragrant, then add snap peas and asparagus. Cook for 3-4 minutes until vegetables are tender-crisp.
Add spaghetti squash strands to the skillet and spread in an even layer. Let cook undisturbed for 3 minutes to develop golden bits on the bottom.
Toss in the shredded rotisserie chicken and cherry tomatoes. Cook for 3-4 minutes until chicken is warmed through and tomatoes begin to soften.
Season with salt, black pepper, and red pepper flakes. Remove from heat.
Top with Parmesan cheese and fresh basil. Toss everything together and serve immediately.