I think in your situation the easiest way would be to use some third-party file storage service, like eg. Dropbox.
Given a path of your file in the local filesystem, eg.
localUri, just share the file with the Share API:
Try out https://snack.expo.io/@sjchmiela/export-the-file. Tapping the button should open iOS’s share action sheet where I, for example, am able to save the file to my Dropbox or Google Drive or Mail.
AFAIR there’s no easy way to just download the file from the iPhone’s file system to the computer if the file is not inside the app you’re currently developing (you’d have to have Xcode and a Mac) or the app has some special capabilities that lets it share some documents to iTunes (https://support.apple.com/en-us/HT201301).