From the Super Mario Wiki, the Mario encyclopedia
Flutter Wings are power-ups that first appeared in Yoshi's New Island. It is gained like the Invincibility Leaf from Super Mario 3D Land, meaning that it only appears after Yoshi loses three lives in a level. Mr. Pipe gives Yoshi this power-up and it turns him into Winged Yoshi. However, Yoshi can only hover, though he can do so as long as he likes. There is a variation of Flutter Wings called Golden Flutter Wings, which acts more like an Invincibility Leaf and are only given when Yoshi loses another life with the Flutter Wings. If all the levels are completed without the Flutter Wings, then there will be a battle with Bowser before Baby Luigi and the Stork are saved.
Even if a Yoshi has already completed their respective level, assuming the Yoshi loses three lives in that level, they will still be offered the Flutter Wings by Mr. Pipe.
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