I created a couple of classes to do exactly this in my module. The one’s you’ll be after are:
AudioPicker: which shows the iOS audio library and returns an array of MPMediaItems which you can then pass to…
AVAssetAudioFormat: which reads samples from the file like any other JUCE AudioFormat.
Make sure you read the docs though as there’s quite a lot of casting to void* due to the Obj-C layer so you’ll have to follow the steps quite carefully.
I haven’t actually used that code in about a year but it was working great so let me know how it goes.