If you're not wishing to use ITunes - and really, why would you if you can avoid it - then VLC player for IOS might be what you're looking for. It plays almost anything. I'm reasonably certain it plays M4A files, and you can import files from many different sources, including dropbox. It does import folders too. I had to use it when playing a book encoded in .FLAC.
It's got a pro version and you'll want to upgrade if you find yourself using it. You can zip the audiobook up and then transfer the zipped file to your phone using, for example, Dropbox.
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Suggestion
If you're not wishing to use ITunes - and really, why would you if you can avoid it - then VLC player for IOS might be what you're looking for. It plays almost anything. I'm reasonably certain it plays M4A files, and you can import files from many different sources, including dropbox. It does import folders too. I had to use it when playing a book encoded in .FLAC.
mp3 autiobook player
I've had some success with MP3 Audiobook Player. It's one of those accidentally accessible apps, so it's not perfect, but it gets the job done:
https://apps.apple.com/us/app/mp3-audiobook-player/id891797540
It's got a pro version and you'll want to upgrade if you find yourself using it. You can zip the audiobook up and then transfer the zipped file to your phone using, for example, Dropbox.
vlc
How am I to use a folder in VLCC?