Data in a runtime database can be edited just as in any other form of FileMaker database. Just as in a regular FMP database, you do need to make sure that the database file is located where the user has "write" permission and the file cannot be set in the OS to be "Read only". Thus, you should have no issues keeping the database on a flash drive.
Save a copy can be scripted with a variable that contains the filename and filepath for the copy created by this step so there should be no trouble scripting a back up save that puts a copy of the file on the flash drive.
But putting everything on a flashdrive is a bit precarious. Backing up the entire flash drive to a computer or additional flash drives in case the flash drive is lost or damaged would be a very good idea.
Here's a thread that describes scripting Save a Copy as to save sequential backups of a file: Saving Sequential Back Ups During Development
The example script here runs from a timer to save a backup every few minutes, but you can run the same kind of script from a button or set up your database to run such a script every time the file is closed.
You may find it useful to read about, and create a USB detailed at http://portableapps.com
Note: this is for windows, although there are links to Mac portable apps.
I have created several USBs with the PortableApps control panel, and included a Runtime of the Campus Productivity Kit.
The portable FireFox and Thunderbird allow you to have your email, addressbook and bookmarks on a thumb drive and carry them with you.
Also functions well as a workable backup. Wuala is a standalone encryptec backup (3Gb) that allows the thumb drive to be backed up on any Win computer.