If a source deals damage to you and/or one or more permanents you control at the same time, Flameblade Angel’s last ability will trigger that many times. For example, if a creature with trample deals damage to a blocking creature you control and you, Flameblade Angel’s ability will trigger two times.

Note that the last ability is optional. Say two players each control a Flameblade Angel, and a source controlled by the first player deals damage to the second player or a permanent they control. The resulting triggered ability may deal damage to the first player, causing the ability of that player’s Flameblade Angel to trigger. That ability may deal damage to the second player, and so on. This cycle will repeat until the game ends or one player declines to use the ability, putting an end to the carnage.