Make the pork: Combine the paprika, 2 teaspoons salt, 1/2 teaspoon pepper, the brown sugar, cumin, mustard powder, onion powder and garlic powder in a bowl. Rub the olive oil all over the pork, then coat with the spice rub. Wrap each tenderloin tightly in plastic wrap and refrigerate 3 to 6 hours.
Make the sauce: Combine the vinegar, 1/2 cup water, the brown sugar, ketchup, red pepper flakes and 1 teaspoon salt in a small saucepan over medium heat. Bring to a simmer, stirring until the sugar dissolves; remove from the heat.
Remove the pork from the refrigerator about 30 minutes before grilling. Preheat a grill to medium high. Cook the pork, turning occasionally, until a thermometer inserted into the thickest part registers 140 degrees F to 145 degrees F, about 20 minutes. Transfer to a cutting board and let rest 15 minutes.
Meanwhile, brush the corn with olive oil; grill, turning, until marked, about 5 minutes. Slice the pork and drizzle with the sauce. Serve with the corn.