Not possible, sorry. The DS doesn't have an operating system running in the background, so only one application can be running at once. Once the game loads, the mp3 player would be shut out of memory entirely.
This type of system does has its advantages however. Because there's no OS in the background, games have complete control over all the hardware, which allows them to do more with less CPU power and RAM.
EDIT: Chris, of course some consoles have multitasking. With the PSP for instance, you can play your own music and a commercial game at the same time because there is an OS running in the background. I believe the XBox 360 and PS3 also have operating systems and thus can multitask in theory, possibly the Wii as well but I'm not sure about that.