Kindle doesn't appear in #VoiceDream as a standard content source. Instead, Amazon's web reader is embedded into the app, and the book text is extracted from the web page to be spoken.
This means that Kindle isn't deeply integrated into the rest of the app, and results in the majority of Voice Dream features being unavailable. You can choose a book and start audio playback, but not access bookmarking, text highlighting, annotations, full-text search, the built-in dictionary, etc. More fundamentally, standard book navigation (e.g. by heading) is not possible either. You can skip by page, and that's all.
I don't know if the features aimed at other audiences, such as finger reading and word highlights, work or not. I would suspect not, given the webview-based architecture, but I haven't been able to verify either way.
Meanwhile:
Playing a Kindle book doesn't register it as your "currently reading" item. If you relaunch the app, or close the Kindle viewer, you have to locate the book in Amazon's web interface from scratch.
Speaking of Amazon's web interface, selecting a book to read happens entirely within it, bringing all of the accessibility issues along for the ride that you may expect from Amazon in 2024.
While Kindle content is playing, the #VoiceOver magic tap gesture causes whatever non-Kindle document you were reading elsewhere in Voice Dream to resume.
You can pause the playback of a Kindle book on AirPods. But when you try to resume, you also trigger the previous non-Kindle document.
On the two books I've tried, there are large pauses in the speech stream at frequent intervals, lasting almost a second. These don't seem to line up with page changes, and I'm not sure what causes them. Maybe something related to scrolling.
I pressed "next page" four or five times in quick succession, to jump past all of the copyright information in a book. Unfortunately, this caused playback to completely stop working, no matter how many times I toggled it.