The key to recognizing an alternate cost is looking for the phrase "rather than pay CARDNAME's mana cost".
In FoW: You may pay 1 life and exile a blue card from your hand
rather than pay Force of Will's mana cost.In Gush: You may return two Islands you control to their owner's hand
rather than pay Gush's mana cost.In Mindbreak: If an opponent cast three or more spells this turn, you may pay
rather than pay Mindbreak Trap's mana cost.The easiest way to remember the interaction is that flashing back a spell is already making use of an alternative cost. I've quoted the exact wording of flashback below for reference, as well as the rule preventing the payment of multiple alternative costs.
702.32. Flashback
702.32a Flashback appears on some instants and sorceries. It represents two static abilities: one that
functions while the card is in a player’s graveyard and the other that functions while the card is
on the stack. “Flashback [cost]” means “You may cast this card from your graveyard by paying
[cost] rather than paying its mana cost” and “If the flashback cost was paid, exile this card
instead of putting it anywhere else any time it would leave the stack.” Casting a spell using its
flashback ability follows the rules for paying alternative costs in rules 601.2b and 601.2e–g.
601.2b If the spell is modal the player announces the mode choice (see rule 700.2). If the player
wishes to splice any cards onto the spell (see rule 702.45), he or she reveals those cards in his or
her hand. If the spell has alternative or additional costs that will be paid as it’s being cast such as
buyback, kicker, or convoke costs (see rules 117.8 and 117.9), the player announces his or her
intentions to pay any or all of those costs (see rule 601.2e).
A player can’t apply two alternative
methods of casting or two alternative costs to a single spell. If the spell has a variable cost that
will be paid as it’s being cast (such as an
in its mana cost; see rule 107.3), the player
announces the value of that variable. If a cost that will be paid as the spell is being cast includes
hybrid mana symbols, the player announces the nonhybrid equivalent cost he or she intends to
pay. If a cost that will be paid as the spell is being cast includes Phyrexian mana symbols, the
player announces whether he or she intends to pay 2 life or the corresponding colored mana cost
for each of those symbols. Previously made choices (such as choosing to cast a spell with
flashback from a graveyard or choosing to cast a creature with morph face down) may restrict
the player’s options when making these choices.
