Does Snapcaster Mage's triggered ability grant flashback to a card that already has flashback?

Snapcaster Mage's triggered ability reads: 'When Snapcaster Mage enters the battlefield, target instant or sorcery card in your graveyard gains flashback until end of turn. The flashback cost is equal to its mana cost.' This ability grants flashback as a new instance of the keyword, regardless of whether the card already has flashback.

Under CR 702.33a, flashback is a keyword ability that lets you cast a card from your graveyard for an alternative cost. A card can have multiple instances of flashback with different costs (CR 702.33b). Each instance is independent, and the player may choose which one to use when casting the spell.

When Snapcaster Mage grants flashback to a card that already has its own flashback cost, the card then has two flashback abilities: its printed one and the new one (equal to its mana cost) granted by Snapcaster. The player choosing to cast that spell via flashback may select either instance.

Practically speaking, granting flashback to a card like Flashback-already-having Runic Repetition doesn't change much unless the costs differ. But with a card like Faithless Looting (which has Flashback {2}{R}), Snapcaster Mage also grants flashback equal to its mana cost {R}, so you could cast it for just {R} instead of {2}{R}.

Concrete example: You have a Faithless Looting in your graveyard with its printed flashback of {2}{R}. Snapcaster Mage enters and grants it an additional flashback equal to its mana cost {R}. You may now cast Faithless Looting from the graveyard by paying either {2}{R} (original flashback) or {R} (Snapcaster's granted flashback).