It's #3.
Flicker of Fate will cause the creature to leave the battlefield and return. FYI, this will trigger any ETB effects related to that creature entering.
When it returns, it will be a new instance of that creature. The relevant rule here is 400.7, which reads:
400.7. An object that moves from one zone to another becomes a new object with no memory of, or relation to, its previous existence.
The creature which had been targeted by Breathe Your Last no longer exists. Since BYL no longer has a valid target, it does not resolve, or "fizzles". The rule here is 608.2b:
608.2b If the spell or ability specifies targets, it checks whether the targets are still legal. A target that’s no longer in the zone it was in when it was targeted is illegal. Other changes to the game state may cause a target to no longer be legal; for example, its characteristics may have changed or an effect may have changed the text of the spell. If the source of an ability has left the zone it was in, its last known information is used during this process. If all its targets, for every instance of the word “target,” are now illegal, the spell or ability doesn’t resolve
Example: Sorin’s Thirst is a black instant that reads, “Sorin’s Thirst deals 2 damage to target creature and you gain 2 life.” If the creature isn’t a legal target during the resolution of Sorin’s Thirst (say, if the creature has gained protection from black or left the battlefield), then Sorin’s Thirst is countered. Its controller doesn’t gain any life.