Combine butternut squash, sweet potatoes, olive oil, salt, and pepper in a storage container. Cover with lid and shake well until fully coated. Place vegetables onto a baking sheet.
Bake in the preheated oven until vegetables are easily pierced with a fork, about 45 minutes.
Place chicken sausage in a large skillet and cook over medium-high heat, turning occasionally, until evenly browned, about 10 minutes. Reduce heat to medium-low; add eggs, spinach, and red pepper flakes. Cook and stir until eggs are set, about 5 minutes. Mix in black beans; cook until heated through, about 1 minute. Add goat cheese.
Fill pita breads with scrambled eggs and baked vegetables.