I had an idea at one point to get a very large flash-drive and move my user files to a flash drive, the idea being I could then take the files anywhere. I've heard of people doing that kind of thing with partitions, where they separate the /usr files from the rest of the system. Of course I would back up the files for safety reasons, but I want to know if it's possible to move an entire user to a flash drive and then use it as if it was a partition.

You could do this; just copy your home folder to the USB, but you will have to edit /etc/fstab on every machine that you plug the USB in to so that it mounts the USB as /home or /home/username. You will also have to make sure every machine you plug the USB in to has an entry in /etc/passwd and /etc/shadow for your user and that all those user entries have the same numeric ID. Then there is the risc of different computers using different versions of software, which may cause trouble with your config files, or different computers running different distros, or DEs, which might cause trouble with your ~/.xinitrc. (Took me ages to get OpenSUSE to accept my Archlinux .xinitrc file.)

Is this feasible if you want to carry your user account with you wherever you go? No.
Is this feasible if you want to have the same user account on all your home computers and your computer at work? Maybe, but you might as well use an old computer as an NFS server from your home. This is a lot safer and easier.
You might also be interested in this thread.

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I'm not aiming to be able to use the drive as a user on any machine. I'm mostly looking to have access to the files on it, even when not running my Linux.

For clarification: Your user's files normally are stored in your user's home directory under /home, /usr stores the applications and their files.

If you don't want to store your user's configuration files, but mere data, why don't you just copy it over? Or mount it to a folder in your user's home directory?

Offtopic: Any reason why this thread is marked as solved?