*FLAD indeed means beauty, cleanlyness. In High
German there was another sound shift, so the outcome of common Germanic *flad is FLAT in High
German (and Kuhfladen has nothing to do with it, it is named because of its flattened form, there also Fladenbrot that is eatable).
Here you can read the details:
http://woerterbuchnetz.de/DWB/?sigle=DWB&mode=Vernetzung&lemid=GF05296#XGF05296 and
http://woerterbuchnetz.de/DWB/?sigle=DWB&mode=Vernetzung&lemid=GF05294#XGF05294 and
http://woerterbuchnetz.de/DWB/?sigle=DWB&mode=Vernetzung&lemid=GF05049#XGF05049