1. In a 6- to 8-quart pan over high heat, bring 3 quarts water to a boil. Meanwhile, rinse chard and remove stems and ribs. Add 2 tablespoons salt and the chard leaves to boiling water. Cook until the greens start to soften, 2 to 3 minutes. Drain, cool, chop, and set aside.
2. Remove tough stems from mushrooms. Rinse and thickly slice caps. Set a 10- to 12-inch frying pan over high heat. Add 2 tablespoons of the olive oil, then the mushrooms and 1/2 teaspoon salt. Stir often until the mushrooms start to brown, about 10 minutes. Remove the mushrooms from the pan.
3. Trim and discard root end and tough green top from leek. Cut stalk in half lengthwise and rinse well under running water. Thinly slice crosswise. Add the remaining olive oil to the unwashed pan over high heat. Add leek and stir often until it starts to soften and colors slightly, 3 to 5 minutes. Add garlic and chile flakes; stir until garlic softens, 1 minute.
4. Add the chopped chard and mushrooms. Stir until hot, about 2 minutes.