In a small bowl, combine chili powder, oregano, cumin, and 1/2 teaspoon salt. Rub spice mixture evenly over flank steak to coat.
In a large skillet, heat oil over medium heat. Add steak; cook until browned on one side, 5 to 8 minutes. Turn; cook until browned on other side, 5 to 8 minutes for medium-rare (reduce heat if browning too quickly). Remove steak from skillet; let rest at least 5 minutes before thinly slicing.
In a medium bowl, whisk together salsa and vinegar; season with salt and pepper. Add arugula; toss to coat with dressing. Divide among four plates; serve with steak, and crumble goat cheese over the top.