It may well do, Dixie, but why would anyone say, "Heavens to....whatever flag" as an indication of surprise? I just can't imagine the French saying, "Heavens to the tricolore!"...in French, obviously...or Brits saying, "Heavens to the Union Flag!"
In the USA, a betsy was also a favourite gun, so the saying might equally apply to that. I can just see John Wayne riding into town, shotgun across his lap, to get his son out of jail saying these words, "Berra lerrim go, Sheriff, or, heavens to Betsy, you'ra a-gonna pay for it!"