01 - Combine ground flaxseed and water in a small bowl; let thicken for 5 minutes.
02 - In a large bowl, mash black beans with a fork, maintaining some texture.
03 - Add diced onion, bell pepper, garlic, oats, breadcrumbs, flax egg, smoked paprika, cumin, chili powder, salt, and pepper to the beans; mix thoroughly.
04 - Divide mixture into four equal portions and shape each into a burger patty.
05 - Heat olive oil in a large nonstick skillet over medium heat and cook patties 4 to 5 minutes per side, until golden and heated through.
06 - In a small bowl, combine vegan mayonnaise, minced chipotle peppers, adobo sauce, lime juice, and salt; mix well.
07 - Toast the burger buns if desired.
08 - Spread chipotle mayo on buns, then layer lettuce, tomato, red onion, black bean patty, and avocado slices; top with remaining bun and serve immediately.