A screenshot of the error message would definitely be helpful.
Also make sure the One Drive software is completely up to date.
Is the One Drive item you are trying to transfer to the USB drive actually stored locally on your Mac, or is it only stored in the cloud. If only in the cloud, then you may need to initiate a download of that file to your Mac before you can perform the transfer. I don't use the One Drive app, so I'm not sure exactly how it handles storage of the files on your computer.
Plus what file system is on the external drive?
Is this flash drive a USB stick or a real SSD?
Do you even have permission to write to the folder on the flash drive? It is usually best to check "Ignore Ownership".
Is the flash drive just a pure data drive, or is it a backup drive such as Time Machine drive?