Did you ever see the film Amelia
,by Mira Nair (one of my fave directors) with Hilary Swank and Richard Gere as Earhart and Putnam? It's beautiful! Their independence and unusual relationship was addressed in it, but it portrays Putnam as jealous of her very close relationship with Gene Vidal, who was Gore Vidal's father (played by Ewan McGregor). It is generally accepted that she and Gene Vidal were lovers. In the film, there is a scene between a very young Gore Vidal and Amelia:
Gore Vidal: Why don't you marry my father? Then I won't be afraid of anything anymore.
Amelia Earhart: I'm already married, to Mr. Putnam.
Gore Vidal: Why can't you be married to Mr. Putnam and my father at the same time?