The reason is that your 360 doesn't have the FLAC decoder built in. When you stream over the network, your 360 is receiving the already decoded audio.
Unless your work laptop is really locked down, it should be possible to install a FLAC player on your external drive and run it from there.
Foobar2000 has a
Portable Installation method that will keep all the files it needs in one folder. Just plug the external drive into your home computer and install Foobar2000 onto it using that install method. You should then be able to run it while it's plugged into your work laptop.
