Heat the olive oil in a skillet over medium heat. Stir in the onion; cook and stir until the onion has softened and turned golden brown, about 10 minutes. Add the garlic and red pepper flakes, stirring until fragrant, about 1 minute. Stir in the chicken broth, Swiss chard, and salt. Cover and reduce heat to low. Simmer until chard is nearly tender, about 5 minutes. Remove lid and increase heat to medium, stirring until the liquid evaporates, about 5 minutes. Remove from heat and set aside.
Heat another skillet over medium-high heat. Warm the tortillas in the skillet for about 1 minute per side. Fill the warmed tortillas with the chard, and top with the queso fresco cheese and salsa.