If I play Flurry of Blades and then pull Elder Dragon from Dazzling Aurora at end of turn, will all the units on the battlefield with damage die?

Ruling: Yes. Elder Dragon's passive ability ("Any amount of your damage is enough to kill enemy units") applies to damage already marked on units before it entered play. When Elder Dragon enters the battlefield via Dazzling Aurora, the 1 damage from Flurry of Blades immediately becomes lethal, and all enemy units with that damage die during the cleanup that occurs before players can respond.

Sequence:

• You play Flurry of Blades, dealing 1 damage to all units. This damage remains marked (damage doesn't heal until the Ending Step).
• During the Ending Phase, Dazzling Aurora triggers and puts Elder Dragon into play.
• Elder Dragon's passive ability becomes active immediately upon entering play.
• Elder Dragon's "When you play me" triggered ability is added to the chain as a pending item.
• A cleanup is processed. During this cleanup, the game checks for lethal damage. Because Elder Dragon is now on the battlefield, the 1 damage is considered lethal, and all enemy units with that damage die.
• Because an item is on the chain, control of battlefields cannot be lost (Rule 187.4.c).
• After cleanup, players receive priority to play reactions to Elder Dragon's triggered ability.

Nuances:

• Players cannot play reactions during the cleanup when units die.
• The damage from Flurry of Blades persists because damage only heals during the Ending Step, which occurs after end-of-turn triggers like Dazzling Aurora.