You cannot perform a Flip Summon during your opponent's turn. A Flip Summon is a way of manually changing the monster's Battle Position. Since it is "manual", it can only be done during your own Main Phase.

You cannot use Ultimate Offering to Flip Summon a monster during your opponent's turn. Ultimate Offering allows you to Normal Summon or Set - while a Flip Summon counts as a Normal Summon, it is not exactly a Normal Summon.

Any force-flip does not count as a Flip Summon. If a face-down monster is attacked during your anyone's Battle Phase, it is considered "flipped face-up" and is not Flip Summoned (or summoned in any way). If your opponent uses Stop Defense, this is not considered a Flip Summon (or any kind of Summon). If your opponent plays Swords of Revealing Light, your monster is not considered Flip Summoned. And so on.