Remove steaks from refrigerator and allow them to come to room temperature for about 45 minutes.
In a small bowl, combine all spices. Rub 2 tablespoons vegetable oil all over flank steak and season well with salt and pepper on both sides. Rub about half of spice mixture all over steak.
Rub remaining 1 tablespoon vegetable oil over corn and coat in remaining spice mixture.
Preheat an outdoor grill to 400F OR heat a large cast iron grill pan on stovetop over medium-high heat. Place steak and corn in a single layer on preheated grill or in pan on stovetop and turn steak and corn occasionally until corn is lightly charred (about 4-6 minutes of cooking) and until steak reaches desired doneness (see blog post for cooking guide).
Remove steak and corn from grill, cover with foil, and allow steak to rest 10 minutes. Thinly slice steak against the grain and arrange on a serving plate with corn.
Drizzle steak and corn with chili lime sauce and top with a few squeezes of lime, cotija, and cilantro for serving. Serve immediately and enjoy!