I want to download some mp3's offf the net & I use Flashget to download which splits up the file to speed up the download, does anyone know if this can damage mp3 files?

If it would damage MP3s, it would damage all other files as well (which it doesn't, i hope). It doesn't matter which filetype you download.

Nope, it doesn't. I use it myself w/o problems. There would be no sense in using download managers which damage the files you load

You could check mp3 file integrity with mp3utility to a certain extend:
Mp3 Utility homepage

Alternatively it would be better to use some kind of CRC check (SFV, MD5)

Scanning with encspot will tell you if there are any sync errors. This might help.