I think I may have gotten Windows Backup to save a system image on a USB flash drive. The flash drive has to be shared because, while the backup program will not accept a local flash drive, it will save to one over the network.
The hard part was getting permissions set right. When Windows formatted the drive the only permissions listed were "Everyone" and it was set to full control. When the drive was shared, those permissions were also "Everyone" and full control. The Backup program insisted it didn't have permission to access the drive. I tried adding my user name explicitly to the permissions list and as owner also, but Explorer kept popping up errors saying I didn't have permission to change permissions. I guess that "Full control" for "Everyone" didn't include me.
So with a properties window for the flash drive open that will not close due to errors, I switched to the backup program and it now seemed to work. Until it asked for a user name and password to access the network. The "Help" for the backup program says if the drive can be seen in "Computer" (it can) the the backup should work (it won't). How did Backup access the drive and determine it couldn't write to it without being able to access the network? Probably more poorly written error messages or confusion due to the drive being both locally and network accessible. Whatever.
The backup error message suggests entering the user name and password for the computer, so I tried that. I put in my user name, but I don't have any password set on this computer so I leave that blank. The "Next" button stays gray. Apparently it's programmed to assume there's always a password. I considered setting up a password, but that wasn't guaranteed to work, and was more hassle than I wanted. I put the cursor in the password box and hit space one time. The "Next" button enabled, I clicked it and the backup process started.
Eventually the backup process completed. That properties window was still open though. I used Task Manager to close it because neither the OK or Cancel button would do anything. After that, I opened Explorer again and checked the properties of the flash drive. The permissions appear to be set to what I had changed them to. I still need to test whether this backup can actually be used. I'm sure that will lead to even more entertainment.