Note taking app that automatically syncs audio and text to Dropbox?

Notability.

I've simply stored its back-up location to one of my Google Drive accounts, and it seems to do everything automagically, in the background. To be fair though, I haven't yet opened anything from the Google Drive account, but a quick perusal, saw the files being stored there. IIRC, should be able to do the same with Dropbox.

I have it on my Mac as well, so Google Drive really is a fail-safe backup, since everything comes through iCloud to my Mac in any event. You would also need to play around with how it works exactly. Again, IIRC, the audio files are separate from the PDF – but you have the option regarding how you want to store the files (i.e. in the Notability app's format; or as PDF and audio).

Notability by default indexes the audio with the note-taking part – which is pretty sweet. Inside the app, when you hit play on the audio, the handwriting/typed text of the note, is faded – but then lights up as the audio part catches up. You can therefore use the audio slider to FWD/RWD to the part of the notes, and hear what was being said at the time you wrote/typed the note. Note-taking bliss!

Hope this helps!