Amazon considers the workings of their Kindle software to be proprietary. There is no technical documentation. (EDIT: Oops, actually I just came across some technical documentation from Amazon for Ion - the underlying data format used by KFX. Posted in the KFX thread in the Kindle Formats forum.)
Automatic hyphenation is part of Enhanced Typesetting (
link). The product description of books sold by Amazon indicates whether Enhanced Typesetting is supported for each book.
It has been discovered that Enhanced Typesetting is only available for books in the undocumented KFX format (
link). It is also known that the KFX rendering software uses a hyphenation dictionary instead of soft hyphens.