No you can't keep an Amazon dolphin. Even in the professional world, it's a big 'no-no'. No place in the US has been able to keep them, and since about 10 years ago, nobody has tried. It's because tey are so rare, and just don't do well in captivity.
I know of one tank that was specifically designed to house three of them. 200,000 gallons designed as a river (great water movement, good depth, lots of swimming room....) Even that turned out not to move forward just because there are still too many unknown factors at this point.