Preheat oven to 375°F.
Cut each squash in half lengthwise. Rub flesh evenly with 1 Tbsp. of the oil. Sprinkle with 1/2 tsp. salt and 1/4 tsp. black pepper. Place squash halves, cut sides down, on a baking sheet. Bake for 50 minutes. Let stand 10 minutes. Scoop out seeds; discard. Scrape inside of squash with a fork to remove spaghetti-like strands. Set aside.
Toast pine nuts in a large dry skillet over medium heat for 2 to 3 minutes, stirring often, until golden. Transfer to a small bowl.
Add butter to pan; cook until butter is browned, foaming, and fragrant, 2 to 3 minutes. Add remaining 3 Tbsp. oil, garlic, thyme, and red pepper flakes. Cook, stirring constantly, until garlic begins to brown, about 1 minute. Add kale; cook until wilted, 1 to 2 minutes. Add spaghetti squash strands, remaining 1/2 tsp. salt, and 1/4 tsp. black pepper; toss well to coat.
Divide squash mixture evenly into 4 squash shells. Sprinkle Fontina cheese evenly overtop. Place back on baking sheet and broil on HIGH 2 minutes, until cheese is melted. Scatter pine nuts overtop; serve with lemon wedges.