Into a large pot over medium heat, add olive oil. When the oil is hot, add the onions and sauté 2-3 minutes.
Add garlic and continue cooking an additional 1 minute.
Stir in the smoked paprika, chili powder, ground cumin, black pepper, and red pepper flakes.
Add light and dark kidney beans, black beans, roasted red pepper, vegan chicken-style broth, undrained diced tomatoes, and barbecue sauce. Stir to combine.
Bring to a boil then reduce heat to low.
Cover and simmer 30 minutes, stirring occasionally.
Uncover and continue simmering for an additional 15 minutes, tor until the chili reaches your preferred consistency.
Serve hot.