Heat oil in large pot over medium-high heat. Add ham; cook, stirring occasionally, until well browned, about 3 minutes. Add pink beans in sauce and chicken broth to pot; bring to boil. Cook, stirring occasionally, until liquid thickens slightly, about 5 minutes. Stir in kale. Reduce heat to low. Cover pot; simmer, covered, until kale is tender, about 3 minutes.
Remove lid. Continue cooking, uncovered, until liquid thickens, about 2 minutes more. Transfer to serving bowl; serve.