Assuming you're running Windows. Make sure the flash drive is Formatted as Fat32. Open it up in File Explorer. Open up the playlist in iTunes. Select one of the songs on it and hit Ctrl+A on the keyboard. It should select them all. Grab and drag all the selected songs over and drop it in the flash drive File Explorer window. That will copy them all.
There might be more automated ways, but that's what I do and it's easy enough. If I want to add music I can just drag on the extra songs. If I want to delete and add a bunch I just wipe the drive and recopy the redone playlist. I was using an iPod in my car for this, but neither of the iPods or even the iPhone 4 I tried worked correctly. The flash drive has worked the best for me on Sync 3. I haven't retried the iPods since the Sync 3 update I did though.