Prepare marinade: Add bloody mary mix, vodka, lemon juice, minced garlic, Worcestershire sauce, celery salt, hot sauce, and horseradish in a mixing bowl and whisk to combine. Set aside 1/4 cup of the marinade.
Marinate the steak: Add marinade to a large casserole dish, or ziplock bag. Use a fork to poke several holes in the flank steak. Add to the casserole dish/zip lock and let marinate for up to 24 hours, but at least 2 hours before cooking.
Heat a cast iron grill pan over medium high heat. If using an outdoor grill, preheat to 450 degrees. Place steak on the grill pan (or grill) and cook for 5 minutes. Flip over and cook for 4 minutes. Place steak on a cutting board and let rest for 10 minutes. Use a foil tent to cover the flank steak as it rests.