I don't know about gender flipping, but there's old Janus. He's the Roman God of doorways, twins, beginnins and endings. He's got a lot going for him in the whole duallity and change thing. Here's a quote from his Wiki
Janus was frequently used to symbolize change and transitions such as the progression of past to future, of one condition to another, of one vision to another, the growing up of young people, and of one universe to another. Hence, Janus was worshipped at the beginnings of the harvest and planting times, as well as marriages, births and other beginnings. He was representative of the middle ground between barbarity and civilization, rural country and urban cities, and youth and adulthood.
Hermaphrodites isn't quite a God, although they're the son of two Gods. Everybody who knows anything about mythology or etymology knows why I'm bringing up them.
Venus/Aphrodites was worshipped by some men who were known to dress in women's clothes and has been known in some myths for taking pity on men and changing them into women.
Dionysus was disguised as a girl by Zeus and raised as a woman for the first years of his life.
Ra from egyptian mythology has been ocasionally seen as genderless.
Atum the first Egyptian god is seen as both male an female. They have kids without needing anybody else.