In small bowl, combine flax meal and 1.5 tablespoons water. set aside for 5 minutes (until it gels).
In food processor, combine black beans, onion, barbecue sauce, salt, paprika and oats. Blend to fully combine. Add flax meal mixture and continue blending. Add chopped walnuts and pulse to combine, leaving some larger nut pieces in the mixture.
Use hands to form four equal-sized patties and transfer to prepared baking sheet. Chill in refrigerator for at least 30 minutes (or up to 3 hours).
Preheat oven 350 degrees F. Bake 20 minutes, carefully flipping burgers halfway through. Serve burgers with mashed avocado, onions and beans sprouts on hamburger buns.