When water reaches a boil, add one tablespoon of salt. Add stems; cover and cook 3 minutes (begin timing as soon as stems are added). Add leaves; cover and cook 5 more minutes. Drain in colander; rinse under cold water until cool. Drain again, squeezing to remove any excess liquid. Coarsely chop.
In a large skillet, heat oil over medium-high heat. Add onion, shallot, and garlic; cook, stirring, until golden, about 2 minutes. Stir in red pepper flakes. Add chard and tomato sauce; reduce heat to medium and cook 5 minutes. Stir in 1/4 teaspoon salt.