Quick-Play Spell Cards are Spell Cards with a Spell Speed 2, and can be activated from your hand during any phase of your turn, as well as during your opponent's turn if they are Set to the field.
Quick-Play Spell Cards may be activated from your hand during your turn; they cannot be activated from your hand during your opponent's turn. They cannot be activated while face-down the turn they are Set. You may chain Quick-Play Spell Cards to cards that your opponent activates during any phase of your turn and, provided that they are face-down on the field, during your opponent's turn.
And as for Flip Summons:
A Flip Summon ONLY occurs when you flip a face-down Defense Position monster into face-up Attack Position.