Combine kale, water, red wine vinegar, and sea salt in a saucepan; cook over medium heat until the kale wilts, about 5 minutes. Remove from heat and drain, reserving the liquid. Set the kale aside.
Combine the reserved liquid and the chicken in the saucepan over medium heat; cook and stir until the chicken is no longer pink in the center, 7 to 10 minutes. Stir the kale, cream, butter, and black pepper through the chicken; cook, stirring occasionally, until the butter melts and the mixture is hot, about 10 minutes. Sprinkle Parmesan cheese over the mixture; cook and stir until the cheese melts and the sauce thickens, 3 to 5 minutes.