(I am not a lawyer and this is not professional legal advice. Do not confuse this article with legitimate legal advice.)
In the United States, you can be sued by anyone for anything (the courts have mechanisms to throw out frivolous lawsuits), and Nintendo most definitely would sue you in civil court for making a significant amount of money from them. So bear that in mind – whether it’s illegal or not, you might be buried under a lawsuit for making them anyway.
But that’s not technically an explanation of the law.
Most of the copyright law as far as distribution goes has not been settled in the courts – it’s theoretical at this point, and the categories of law has yet to catch up with the categories of software. Amiibo is a great example of this: the law only covers software, not physically-stored software meant to be used in conjunction with previously-purchased physical components and software. There’s about four more layers of complexity to it that has no law for it.
Instead, we’ll focus on the distribution aspect of the software, and assuming you’re selling the cards. Amiibo are copyrighted works and probably fall under the category of commercial software, making their distribution illegal (because Nintendo presumably doesn’t want others to distribute amiibo files). This is not an absolutely certain conclusion, because amiibo also exist as physical figures and cards, and physical objects fall under different law. It is not 100% certain that amiibo cards or distribution is illegal if there’s a physical component to them. The law on this simply isn’t settled.