I have a bada phone. It receives radio via an FM (frequency modulated) antennae. It can record this natively (don't know about publicly available API's). http://www.technostarry.com/mobiles/fm-radio-record-samsung-wave-bada-phone/
I have an Android device. It receives radio via an FM antennae. It can not record this.
Why is this so? I've looked at other sites which suggest that the reason is the FM radio signal is never digitized, but were it digitized then, in theory at least, the data would be accessible.
Sorry if this comes across as discussion-like. I just thought this site could do with a thread on this. The one I found has an incorrect answer that suggests the person that accepted it has conflated FM with internet radio, How to record an FM audio in android?.
AFAIK an analogue radio is not a standard component for Android, meaning that stock android does not provide APIs to take advantage of an analogue radio. Any phones that include this functionality have had this functionality added by the OEM. Its then up to the OEM to provide APIs for developers to take advantage of this non-standard functionality.
If the OEM doesn't provide API's you can always try decompiling the radio app that ships with the phone to figure out the appropriate function calls.