The Audible title in question has to support 'Whispersync for Voice-Ready'. In many cases, that is not the case. For example Hillary Clinton's new book is available in ebook and audible formats, but doesn't support this. Same with Diana Gabaldon's new book. I don't know of cases where support was added later on, but that seems possible. However, again referencing Gabaldon's Outlander series, some of her audible titles support it and some do not, even a couple of years following the launch of 'Whispersync for voice'. So there may be licensing or technical issues that get in the way of having more complete coverage.
At this point you cannot use the Kindle app to listen to Audible books unless you also own the ebook (and again, unless the audible edition supports W4V). So you still need the Audible app. In theory I'd like to use one app instead of two but only if that could be done without slowing app launch significantly, and preserving features etc. I doubt there are plans to get rid of Audible app.
It is really inconvenient to 'upgrade' with the audiobook on iOS, given that Apple's policy prevents amazon from offering links to storefront (without in-app purchase and sharing revenue with Apple). Probably the easiest way is to go to the 'matchmaker' page with Safari:
https://www.amazon.com/gp/audible/matchmaker
The Android Kindle app has this built in and when you are reading a book you can purchase directly.