In a Dutch oven, heat olive oil over medium-high heat. Add sausage and bacon and cook until sausage is browned and bacon is crispy. Remove with a slotted spoon and set aside.
Add onion to the grease in the Dutch oven and cook until soft, about 5 minutes.
Add garlic and cook 1 more minute.
Add tomatoes, chicken broth, black-eyed peas, dried thyme, and red pepper flakes.
Season with salt and pepper.
Bring to a boil and reduce heat to a simmer. Cover partially and cook until black-eyed peas are soft, about 1 hour to 1 hour and 15 minutes.
Return sausage and bacon to Dutch oven.
Add kale one handful at a time, stirring it in as you go. Once kale has wilted, it is ready to serve.