Is the quality of sound retrieved from a flash drive equal to that from a burned DVD?
If you’re simply comparing audio files stored on the two different media formats, I don’t think you’ll notice a difference in sound quality. Where you’ll notice a difference is in the ease of copying material to a USB drive as compared to burning optical media. Additionally, extra capacity along with the ability to make changes to the file structure on the USB drive and update its contents make it a clear winner over optical discs.
Be aware that neither provide gapless play when playing audio files such as WAV and FLAC. Also be aware that navigation of folders on the USB drive is going to require some patience on your part.
If you were to burn your files as a DAD (up to 24/96) or DVD-A (up to 24/192) disc rather than simply use the disc for file storage, you could overcome the gapless issue. In this case, you’ll want to do a bit of experimentation to find an authoring method that makes it easy to play the disc on the DMP.
If you have a sizable collection of audio files, you might consider the purchase of a Bridge II - it will greatly simplify playback.