Actually, if we're using mythical beast analogies, the multi-headed hydra would be a more fitting creature to compare Flappy Bird Family to, as this new form features multiple flapping birds thanks to the addition of multiplayer.
Yes. Flappy Birds Family, now available on the Amazon Appstore for Android - but curiously absent from iTunes and Google Play - is a cross between a phoenix and a hydra. A hydrenix (or phoendra), if you will. If you've got access to the Amazon Appstore, you can capture it free of charge.