I don't claim to know much about anything, but oddly, I do know a little about this. I don't know about the laws or the legality of owning or keeping them but I do know what it takes to keep them.
I'm an architect and I've done a lot of work for the San Diego Zoo and San Diego Wild Animal Park. A few years ago we redesigned the flamingo exhibit at the entry to the San Diego Zoo. The keepers and curators worked with us and told us how much space and how deep the water should be and stuff like that.
It comes down to keeping predators out (could be difficult), keeping the birds in (not too difficult), giving the birds plenty of room so that they don't feel pressured or stressed from people (about 50 feet between you and them), lots of water that's 6-12 inches deep (if I remember right), a HUGE filtration system - REALLY HUGE or dump and fill every three days, a nesting island with special soil mix and irrigation below to make it just the right kind of muddy...
After all of that, I don't think that they do well in solitary confinement...I might be wrong but I'm thinking that they need a big flock or as it is properly known - a flamboyance of flamingos.
