Heat oil in a medium saucepan over medium heat. Add onion, garlic, and red-pepper flakes and cook until tender, 6 to 8 minutes. Add roasted peppers and stock. Bring to a boil; reduce heat and simmer, 10 minutes. Let cool slightly, then puree in a blender until smooth. Season with salt.
In a small bowl, mix together quinoa, red onion, avocado, and cilantro. Season with salt. To serve, ladle soup into bowls, top with quinoa salsa, and squeeze with lime.