Heat oil in a large frying pan over medium heat. Add red capsicum, onion, carrot and garlic; cook and stir until lightly browned, 8 to 10 minutes. Add mushrooms; cook for 1 minute.
Transfer mixture to a pot. Add mixed beans, diced tomatoes with juice, chilli powder, flaxseeds, cumin, oregano and black pepper; stir well. Bring to a boil; simmer uncovered, stirring occasionally, until flavours combine, about 30 minutes.
Use 2 cups cooked beans in place of the canned beans if desired.