I wish I had a good answer for you, but Comenity, with handling this card, just seems to take a pretty ghetto approach for lack of a better word. Why are they issuing a card in 2019 with no chip? They're a major partner for many, many store/cobrand cards and they can't afford a chip? Beyond that, a lot of people had issues even applying for the AKC card because the site would crash during the application.
It doesn't surprise me that the personalization feature doesn't work as advertised. Comenity just being Comenity unfortunately.
No clue on the AKC visa question, but just thought I would mention that my hideous comenity true value discover card issued in 7/2019 does not have a chip either.....ghettofab.