Bring water and rice to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until rice is tender and liquid has been absorbed, 20 to 25 minutes.

Heat oil in a large pot over medium-high heat. Add carrots, celery, onion, bell pepper, and garlic; cook until tender, about 5 minutes.

Add black beans and liquid from can, chorizo, chicken stock, picante sauce, bay leaves, paprika, vinegar, cumin, sugar, salt, black pepper, and pepper flakes; bring to a boil. Reduce heat to medium-low, cover, and simmer until beans are soft, about 30 minutes.

Uncover the pan; continue cooking until mixture reaches desired consistency, about 20 minutes more. Discard bay leaves, taste, adjust seasoning.