After an extensive search in user groups on Google and other avenues. I could not find a Linux version of OpenOffice.org Portable. From my research I gather that most Linux users really don't want to use a portable version of OpenOffice.org. The general consensus is that you can just install it from the repositories so why do you need it on a flash-drive.
Most users who do want to use OpenOffice.org on a flash-drive tend to either use the Windows version or use a Linux OS installation which includes OpenOffice. For those who want to use the Windows version directions can be found below. For people who want to use a Linux OS on a flash-drive see this article.