Cook the gnocchi according to package directions. Drain and set aside. To keep the gnocchi from sticking together, toss it in a small amount of olive oil, if desired.
Heat the 2 tablespoons olive oil and 2 tablespoons butter in a large skillet over medium heat. Add the shallot and garlic and cook for 1-2 minutes, until soft.
Add the thyme and oregano, as well as the red pepper flakes, if desired. Add the flour and stir until fully incorporated.
Add the white wine and broth to the skillet and whisk to combine them with the flour. Bring to a simmer and cook for 4-5 minutes, until slightly thickened.
Add the chicken, heavy cream, and Parmesan, and simmer for another 4-5 minutes, until thickened.
Add the drained gnocchi and mix to combine. Stir in the baby kale. Add salt and pepper, to taste.