I appreciate your efforts Barbara,
The eastern European connection had crossed my mind also, and given the
movement of labour and armies it would be natural for a name to cross
borders. When I started to research my grandmother's surname 'Flemme'
(pronounced Flemm-ee), I noticed there is a "FLEMME FOREST" in Italy, which
leads me to think that the Flemme surname wasn't common in Austria either.
Thank you once again
Rena