Hello, I'm an experienced iOS developer and yes, there is a straightforward solution for this, what you need is called Amazon Transcribe, which is the Speech to Text API.
Relevant Skills and Experience
Close to 6 years of iOS development, plus countless other projects
Proposed Milestones
$258 AUD - App completed as described
Additional Services Offered
$49 AUD - Send to App Store/Entreprise Distribution/Ad Hoc distribution
Ok, so I'll create the app with a single screen for you to tap a button and start a recording using AVFoundation. This recording will be sent to Amazon and transformed into text with Transcribe. The resulting text file will be shown to the user on another screen or popup. There will be some place to set up some configuration parameters, like the AWS account, etc. Also, note that use of the Amazon service may not be free. I need just a few days to get this done.