Flanking is an interesting ability that was introduced in the Mirage block and can be found on primarily white, black, and red creatures. When a creature that has flanking is blocked or becomes blocked, the blocking/attacking creature get's -1/-1. A creature with multiple instants of Flanking triggers separately.
If a creature that blocks a creature with flanking, and the creature dies from the -1/-1, it never deals damage to the attack/defending creature with flanking, even if it has First Strike. However, it's still considered to be blocked, so damage will not be dealt to the opponent unless it Trample.