If you just want the fly over (haha, see what I did there?) the Huma bird is a Sufi or Persian legend/tale/mythological bird that contains both male and female bits (apparently one leg and one wing of each gender, which is confusing because in some legends it has no legs) and even it's shadow is considered lucky. It flies high above the earth and occasionally swoops down to pick a king or two (again, depending on who you ask) and then goes back up to the clouds.
Well, at least it's considerate enough to have lucky feathers, instead of the traditional way I was taught birds give us luck...