I haven't found a professional, full-length narration on Audible, Spotify, or Google Play. There are some text-to-speech robot-read versions floating around on some free audiobook sites, but the quality is usually awful and honestly not worth the time. It's a shame because the epistolary style could work really well in audio if done right.
Your best chance might be to check if the publisher has any plans for one, or see if it pops up on services like Scribd eventually. For now, I ended up just reading the ebook. The novel itself is a slow, introspective kind of historical fiction, so maybe it's better suited to quiet reading anyway. I remember some passages about letter-writing that felt oddly fitting for the format I was stuck with.