An effect that gives flashback to an instant or sorcery card in your graveyard stops applying once that card has left the stack. The card won’t have flashback while exiled and can’t be the target of Runic Repetition (unless it naturally has flashback).

A card that’s exiled face down doesn’t have any characteristics or abilities, so it can’t be the target of Runic Repetition.

The card could have been exiled for any reason, not just because it was cast using flashback.