andean flamingo

This is the James flamingo in with the Andean flamingo

Looks more like an Andean than a James' (Puna) Flamingo.
If it was a James' shouldn't it have more yellow on the beak, less black on the tail, and more red around the eye? This bird doesn't appear to have those, so would be an Andean as titled.

I am going by the red edging to the beak as Andean don't appear to have this and James do but If I am incorrect will be happy to be corrected.

It seems to be more prominent in James', however it seems Andean do have it as well.

See this picture for example Andean Flamingo photo: A bird standing in the water. | the Internet Bird Collection

I stand corrected many thanks for the info on the beaks

Are there any James or Andean flamingos in captivity in S America?