Make the chicken: Season chicken thighs with salt and pepper and coat with 1 cup BBQ sauce; either cook in a slow cooker on low for 4 hours then shred and return to sauce and cook 30 more minutes, or bake at 400°F for 20–25 minutes until cooked through, then shred and toss with sauce.
Prepare the squash: Cut ends off the spaghetti squash and slice in half lengthwise; scoop out and discard the seeds.
Cook the squash flesh: Place squash halves cut-side up in a microwave-safe dish and microwave 12–15 minutes until the flesh shreds easily with a fork; alternatively roast in a 425°F oven until tender.
Shred the squash flesh with a fork into noodle-like strands, leaving the shells intact to use as boats.
Preheat the oven to 350°F and heat 1 tablespoon olive oil in a large skillet over medium heat.
Sauté garlic and red pepper flakes for about 30 seconds until fragrant, then add the diced red onion, season with salt and pepper, and cook about 5 minutes until softened.
Add the shredded spaghetti squash, 1 cup shredded BBQ chicken (or desired amount), and 1/2 cup BBQ sauce to the skillet; stir to combine and adjust salt and pepper to taste.
Place the empty squash shells in a large baking dish and evenly divide the squash and chicken mixture between them.
Top each stuffed squash with shredded mozzarella and smoked gouda, add a few small dollops of extra BBQ sauce if desired, and arrange reserved onion rings on top.
Bake at 350°F for about 10 minutes until the cheese is melted and bubbly, then broil 1–2 minutes if you want the cheese browned.
Garnish with chopped cilantro and a sprinkle of red pepper flakes before serving.