What sort of privacy implications? I'd imagine that Anki data would be relatively privacy-concern free, as it contains no PII, and for the AnKing decks, all of the content is standardized and so wouldn't contain personal notes. Though, having never worked with this data, please let me know if I'm wrong!
Also, having used those decks in the past, and downloaded the add-on/look at the monetization structure of developers like the AnKing, I would be very surprised if aggregate data on review statistics wasn't collected in some way. I.e., if the AnKing is collecting this data already to design better decks/understand which cards are the hardest—probably to target individual support—then I imagine that collecting some de-anonymized version of that data wouldn't be too much of a stretch.
Plus, considering that all of the developers of AnKing-style decks are all doctors, they probably have a pretty good grasp at handling PII and could (hopefully) make pretty sound decisions on whether to give you access :)
You're right, it might work by restricting to just AnKing data. My concern was around other, possibly personal, cards making their way into the dataset.