Bring potatoes to a boil in a medium saucepan of well-salted water. Reduce heat and simmer until tender, about 10 minutes. Stir in kale and cook until wilted, 1 to 2 minutes. Drain.
Heat oil in a large pan over medium-high heat. Add potatoes and kale. Cook, stirring, until potatoes are golden brown, about 5 minutes. Add garlic and red pepper flakes and cook about 1 minute. Season with salt and pepper; serve warm or at room temperature.