Much like hanger steaks and skirt steaks, flap steaks should be well-marinated to help them break down (fruit juice works well here), prepped well, cooked carefully, and always cut across the grain.
Do not use until it is cold. Put the bavette steak into a resealable freezer bag, pour in the cold marinade and squelch it about so that the thin steak is covered on both sides, then seal ...