Place a large pot over medium heat and add the chorizo slices. Cook until the edges brown and the fat renders out, about 5 minutes.
Add the diced onion to the pot and stir. Cook until the onion softens, about 4 minutes.
Stir in the minced garlic, smoked paprika, and red pepper flakes. Cook for 1 minute until fragrant.
Pour in the diced tomatoes and chicken broth. Season with salt and black pepper. Bring the mixture to a simmer.
Add the chopped kale and stir it into the broth. Simmer for 10 minutes until the kale is tender.
Taste and adjust salt or pepper if needed. Ladle the stew into bowls and serve with slices of crusty sourdough bread on the side.