Some Internet radio stations do not provide mp3 streams or similar open access to their content. Flash players are being used by some of the best Internet radio stations. Audio recording is not easy just having a Flash audio stream. But you can always record the audio from the “sound card” directly (modern PCs don’t have sound cards, of course). You can record directly “from the speakers”, using Audacity.
The Audacity Tutorial describes the required setup. Of course, this has the disadvantage that you cannot record an audio stream in the background, while listening to another stream.