You can now open local music files from your phone using Audiomack and listen to them in your Audiomack app library. Currently, this is only available on the latest Android version of the Audiomack app.
1. Open your phone's file manager
2. Select the audio file you want to listen to on Audiomack
3. Tap the menu button next to the file, and select "Open With > Audiomack"
Here's a quick guide: