BeerSmith is set to use \Documents\BeerSmith2 as the default directory and it's baked in. Using the BeerSmith cloud lets you work on just a recipe at a time and share it. The cloud doesn't let you store new profiles or inventory, though.
To use the flash drive, you'll have to copy the \Documents\BeerSmith2 folder to the flash drive. Later, you can open BeerSmith on a new machine, then File > Open File > Locate the Drive \BeerSmith2 > Recipe.bsmx. Don't panic that you'll see 5 more recipe files. These are archives.
Once open, you'll see all of your recipes and folders. Work on them. When done, be sure to use the "Close" button. This will prompt a save of the recipe folder back onto the flash drive.
This limits you to working from just the flash drive. Recipe modifications on either computer or the flash drive become independent of each other of you don't work exclusively from one source. Periodically, just copy the flash drive back to the computers.