Do you have any other backups or copies of the files?
Depending on how important the files are you may want to consider a professional data recovery service such as Drive Savers or Kroll Ontrack. Both companies offer free estimates and are recommended by the major OEMs such as Apple.
If you are not willing to pay for a professional service, then my advice is to make a bit for bit clone of the USB drive and work on trying to retrieve the items from the raw image file. This way you can make multiple copies of the raw image and if you make a mistake, you can try again on an untouched image. You could try using the Terminal and the "dd" command to do this, but if the USB drive produces any errors, then I would suggest using GNU ddrescue to create the clone. Working from the clone is best especially if the drive has a physical failure.
You can then try the free apps PhotoRec or TestDisk to try recovering the data. You may need to use Disk Utility or Disk Warrior to repair the damaged file system. Data Rescue is a paid app which I've used in the past. TestDisk does not need to be able to mount the drive to work.
It is hard to say if you will be able to recover anything from a flash drive.
Keep in mind the more you try recovering stuff from the physical flash drive, the more likely you will corrupt it further or the drive failure will get worse and even a professional service won't be able to help.
