The swastika (right-facing) did become the more common form for the Nazis apparently.
From Wikipedia (Swastika entry):
While the DAP and the NSDAP had used both right-facing and left-facing swastikas, the right-facing swastika was used consistently from 1920 onwards. Ralf Stelter notes that the swastika flag used on land had a right-facing swastika on both sides, while the ensign (naval flag) had it printed through so that a left-facing swastika would be seen when looking at the ensign with the flagpole to the right.[104] Nazi ensigns had a through and through image, so both versions were present, one on each side, but the Nazi flag on land was right-facing on both sides and at a 45° rotation.
