Flamingos do have to fear predators in their day to day life. Animals such foxes, raccoon's, vultures, and any animal bigger than they are most likely prey on the unique bird.
Do humans pose a threat on Flamingos??
Diseases are not greatly known for affecting flamingos, but illness is. Illnesses that affect flamingos include tuberculosis and avian flu, these are both common human respiratory illnesses but are found in flamingos too. There is one found disease that had been found and that is Newcastle Disease which is an infectious viral fever that kills the birds quickly if they catch it.
Because people do not eat flamingo, and other areas of them are not used for any other purpose, the birds are mostly safe from humans.