Combine ground flax seeds and water in a small bowl. Set aside for 5-10 minutes to thicken up.
Meanwhile, in a food processor, add the bell pepper, white onion, garlic, and black beans. Pulse until peppers and onions are chopped very small and beans are mashed but still a bit chunky with a few whole beans still intact.
Add bean mixture to a large bowl. To it, add the thickened flax mixture, bread crumbs, and seasonings. Stir to combine all ingredients.
Using a 1/2 cup, form the mixture into 8 patties.
Heat a large non-stick skillet to medium heat. Drizzle olive oil in pan. Brown patties in skillet for 5-7 minutes on each side until browned.