On a work surface, place a pork chop between 2 sheets of plastic wrap and, using a meat mallet, pound 1/4 inch thick; repeat with the remaining chops. Slice into 1/4-inch-thick strips. In a shallow bowl, whisk together the flour and salt; add the pork and toss.
In a large nonstick skillet, heat 3 tablespoons oil over medium-high heat. Shake off any excess flour from the pork and arrange in a single layer in the skillet. Cook until browned and crisp on one side, about 3 minutes; turn and cook, stirring, until browned all over, 2 to 3 minutes. Transfer to a plate.
Add the remaining 1 tablespoon oil and the cabbage to the skillet and cook, stirring occasionally, until the cabbage begins to brown, 2 to 3 minutes. Add the garlic and ginger and cook, stirring, for 30 seconds. Stir in the teriyaki sauce, then toss with the pork and mangoes. Top with the bean sprouts.