How does the Miracle mechanic interact with Flashback?
Snapcaster Mage: Bold for emphasis.

Flash
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. (You may cast that card from your graveyard for its flashback cost. Then exile it.)

The flashback cost will be the mana cost of the card, shown on the top right corner of the card. Alternative costs such as the Miracle cost are irrelevant.
But what if you had a Bösium Strip in play?

Miracle {cost} (You may cast this card for its miracle cost when you draw it if it's the first card you drew this turn.)

The Miracle cost may only be payed if that card is the first card drawn from your library in a turn, and only when you draw the card. Clearly if the card is in your graveyard, it cannot be drawn, so the replacement effect for the casting cost will never apply.
As an aside, note the implications for a card like Future Sight. If you play the top card in your library that's revealed, you won't be drawing it, so you must pay full cost.