Prepare the marinade by combining the marinade ingredients in a bowl or measuring cup until blended.
Place the flank steak in a large resealable plastic bag and pour the marinade over it, removing excess air before sealing.
Refrigerate and marinate for several hours or up to 24 hours.
About 30 minutes before grilling, remove the steak from the fridge and let it come to room temperature.
Oil the grill by dipping a paper towel in olive oil and using tongs to rub it over the grates, then preheat the grill to medium-high.
Grill the flank steak to desired doneness: about 4–5 minutes per side for rare to medium-rare, or about 6 minutes per side for medium; use an instant-read thermometer to check (140–145°F for medium-rare, 155–160°F for medium).
Remove the steak from the grill and let it rest for about 5 minutes, loosely tented with foil if desired.
Slice the steak thinly across the grain and serve hot with lime slices to squeeze over the meat.