Unfortunately, no, there isn't.
The only way to install music to your hard drive is to 'rip' it off of a CD.
However, what you should be able to do is take your flash drive, plug it into a computer, and burn the songs onto a CD. Then you can take that CD and rip it to your hard drive.
Yes, I realize that this is a lot of work, but unfortunately if you want to 'permanently' install your music on your 360 it's about the only way to go.