For some years now I've been keeping a pocket size voice recorder in my nightstand drawer. When I awake and remember a dream, I record what I can remember. Normally the recording begins with the most recent part of the dream (right before waking), but I usually find that the act of concentrating on what I remember stimulates more memories of earlier dream segments. Most recordings run 2-4 minutes, but some dreams have taken as long as 10-12 minutes to record.
Every few months, when the recorder's memory fills up, I dump it to a hard drive on my main desktop. That drive is eventually backed up to an offline portable drive.
I don't do cloud storage, so none of this ever leaves my home. (Much as I'd like to have a backup stored offsite, there's no other place I can think of which has the same level of legal protection as my own home.)
Which brings me to my point, I guess. This app does have some clear advantages over my system, but privacy isn't among them.
Unless some spook breaks into my house and plants a trojan on my computer, I'm the only one who will ever have access to my dreams, some of which are pretty damn personal.
On the other hand, anything on a mobile phone is inherently insecure. I have my doubts that this app can guarantee the kind of privacy I want for my dreams. Prove me wrong.