Arcane melee and Flashback

[tyrkae]

Question:
If i had Arcane Melee out and i had something with a flashback casting cost I would be 2 less
Example Faithless Looting would cost only 1 red mana to cast from the graveyard

[Segoth]

Cost reductions (or increases for that manner) are still applied to alternative casting costs, so it would indeed reduce the casting cost of instants or sorcery's that are cast using flashback. So in your example the Faithless Looting would be only one red mana to flashback.