I believe their is a command line switch (-portable?) that tells flashfxp not to use registry information. In such a case (not reading the data file location from registry) i would assume it falls back on using data files in the same directory as the executable.
The easiest way to do it is to simply use our portable setup.
But if you really want to do it manually its simply a matter of creating a zero byte file named "flashfxp.portable" in your FlashFXP folder, if this file is found on startup FlashFXP uses the same location to store your data files and does not store any values in the registry and runs in portable mode.