Is the subject line question possible? I can’t even figure out where the downloaded file is on an iPhone 11 running IOS 16.0.2 to access the actual music file, as a file (EDIT: I know where it is to play it), let alone transfer it. The file has to be on my phone, is it made unaccessible for purposes other than playing it from the Mixcloud app.?
It seems like mixcloud, like Tidal, Qobuz, and other streaming services, download files to their protected area and they are not available to be played by other applications. However, I could be wrong as that was from just reading a couple of minutes on their site.
The best option it to ask Mixcloud if it is possible to do what you want.