The only DL/AF/KL itinerary all the way to VIE that would get you flat beds in Business over the water is the DL JFK-CDG flight, which unfortunately switches back to the unrefurbished 763ER after the Sept 4 flight...I assume you are going later in the month?

Otherwise, you will have to interline with another non-ST airline. If you do that, then you can take DL flat beds through LHR (all US gateways), FRA (all US gateways), MUC (ATL) or BRU (JFK). From LHR, connect via BA or OS; FRA via LH or OS, MUC via LH or OS, BRU via SN or OS...