Cut out center ribs and stems from chard, then thoroughly wash, along with leaves, in several changes of cold water. Cut ribs and stems crosswise into 1/4-inch-thick pieces and coarsely chop leaves.
Cook kielbasa in oil in a 5-quart heavy pot over moderately high heat, stirring occasionally, until golden, 2 to 3 minutes. Transfer with a slotted spoon to a bowl. Cook chard ribs and stems with salt in fat remaining in pot over moderate heat, stirring occasionally, 3 minutes. Add garlic and cook, stirring, 1 minute. Add chard leaves, water, and red-pepper flakes and simmer, partially covered, until chard stems are tender, about 5 minutes. Remove lid and stir in kielbasa.
Cook pasta in a large pot of boiling salted water until al dente, then reserve 1/2 cup pasta-cooking water and drain pasta in a colander. Add pasta to chard mixture with cheese and salt to taste and toss until combined well. Thin with some of reserved pasta water if necessary.