Well, if you have your Windows side FS2_Open installation in a decent shape... Easiest solution is to
$ cp -R /media/<windows-partition>/path/freespace2 /path/freespace2
and then fix the rights as needed with chmod. Then simply either find a linux build of FS2_Open or compile your own. Slap that file into /path/freespace2, run it once, quit, do some configuration (there's a file in ~/.fs2_open/ after running the game once, but I don't remember that file's name - there are better instructions in
FreeSpace Wiki).
There's no official launcher applet for Linux yet as far as I know, so you'll likely have to write (or copy-paste) a script that will run the executable with desired command line options... Also, as you transfer the game directory from Windows partition, there will be a configuration file /path/freespace2/data/cmdline_fso.cfg, which will contain the latest command line options selected in Windows before copying the files to Linux partition. You can open it up and edit the command line options - those options will then be applied every time you run the game.