Although the baby bird that was fed to the eaglets on April 4, 2014 certainly resembled a flamingo nestling, Flamingo Gardens reported that all their birds were accounted for. (Sorry for the late post but I forgot to enter this information at the time).
Here is a link to a series of photos of flamingo hatchlings. While the prey bird's bill seems to fit, its legs do not much resemble those of a flamingo. Still a bit of a mystery as no experts have ventured any other opinions. I'll stick with identifying it as a Little Blue Heron nestling.
See:
http://www.flickriver.com/photos/nathaninsandiego/tags/babyflamingo/