It is possible.
While the BlackBerry won't handle flash, there are applications/web sites, out there that allow you to listen to radio stations. They stream the audio in a format the Blackberry can handle. Some are free, some are not, check the 3rd Party Apps forum for more info.
I use moodio (Welcome to Moodio! | Moodio
), it's a free site with a great deal of stations available, and it has the ability to allow users to add stations if they are not currently supported. If it's not listed you'll need to find the direct url to the audio stream. The web site has a guide to do this.
I'd recommend you have an unlimited data plan no matter what program you use. Not everything is supported. Do some research at moodio's site and the 3rd party apps thread here at bbforums.