completely different use case. DNG is a pre-processed RAW format. (debatably) useful for recording the digital bit data off a sensor. It may also contain a processed jpeg preview.
FLIF is a final processed image for viewing on the web. I doubt it would be better than a PSD of TIF for printing though.
in other words, start with a DNG*, do some post processing and output a FLIF.
*As an aside, I do not see the advantage of DNG from a consumer point of view. If your camera does not natively save as a DNG, converting is just an extra step for no real gain.