Using a spiralizer, cut zucchini into zoodles; set aside.
In a large bowl, mix together ground chicken, 2 cloves minced garlic, egg, Parmesan cheese, parsley, and red pepper flakes; season with salt and pepper. Using a cookie scoop form into tablespoon-sized meatballs.
In a large skillet heat olive oil over medium heat. Cook meatballs until golden on all sides and cooked through, about 10 minutes. Transfer to a pie plate and loosely cover with foil.
Melt butter in the same skillet, add remaining 3 cloves minced garlic, cook until fragrant about 1 minute. Add zoodles to the skillet, toss to coat in garlic butter.
Add meatballs back to the skillet, heat until warmed through about 1-2 minutes. Garnish with Parmesan cheese and serve.