Playing Songs on the DS is possible with the use of flash card and the correct software. You need to use MoonShell to play your MP3 songs. Most users will have the Moonshell if you are using DSTT, R4 or others flash card.
If you do not have it, you can download Moonshell by clicking here>>>
Just unzip and paste the moonshl folder and _moonshl.nds to the root of your memory card.
Go to your flash card menu and click on moonshell.nds. Upon entering the software scroll to your folder where you kept the songs and Press button A to enter. Just Press A to play the songs and B to stop playing the songs.