even though the Kindle runs Linux, multitasking is a major problem. Getting programs to run on the top window is a PITA. I don't think anyone has been able to do what you want - music while reading.
Since I'm in the USA, I use pianobar or pianobarfly sometimes on my Kindle to listen/record streaming from Pandora. Mplayer is used to play the songs downloaded. If you want just streaming radio, mplayer can do that well, just not while reading
(at least I can't, maybe you can?)