the quest isn´t glitch, I did it just yesterday. I notice that the flamingos one screen below the null chamber drop the feathers more common than other flamingos in village green though.
If they still don´t drop feathers, take a break in barton town till your ghi bar is full as it add a luck bonus. Fitness, Coyote Spirit, Divinity, Fortunes Favor and the Angel Set can also increase your Luck, to obtain more loot.
make sure that the animated appear with a green or at least blue background to you, otherwise they won´t drop anything.