It's really hard to say. Godzilla has his atomic breath and great strength, but King Ghidorah has three heads and can fly. In a straight - up fight, if Godzilla can get in close and use his physical strength, he might have an advantage. But if King Ghidorah can keep his distance and use his aerial attacks and energy beams from all three heads, he could be the victor.
One idea could be a story where Godzilla and King Ghidorah have to team up against an even greater threat from outer space. This would force their natural enmity aside as they realize the common danger.
One common theme is the power struggle. Given King Ghidorah's already formidable nature, in fanfiction with a female version, there might be a focus on how she wields her power, whether it's against other kaiju or in a more complex political or social structure within the kaiju world. Another theme could be redemption. Maybe the Female King Ghidorah starts off as a villain but then has a change of heart.
One popular 'godzilla x ghidorah fanfic' is 'Clash of Titans: Godzilla and Ghidorah'. It has an interesting plot where they team up against a common enemy. The author does a great job of describing their interactions.
Another theme is the relationship between good and evil. Godzilla is often seen as a protector, while Ghidorah is more of a destroyer. Fanfics may play around with this perception, showing that there could be more to their natures. In some, they might even switch roles to some extent. This theme makes the stories more thought - provoking.
In a King Ghidorah x Mothra fanfiction, a possible plot could be that King Ghidorah is somehow injured and Mothra, being the more benevolent of the two, decides to heal him. As she heals him, she also tries to change his evil ways. This could be a story of redemption for King Ghidorah, and how Mothra's kindness can have a profound impact on even the most evil of creatures.
Well, a fanfiction could be set in an alternate universe where King Ghidorah and Mothra are the last two of their kind. They have to find a way to repopulate their species, but their natural instincts are so different. King Ghidorah is more about destruction and dominance, while Mothra is about life and harmony. This conflict could be the central theme of the story, exploring how they try to overcome their differences for the greater good of their species.
In the world of fanfiction, it could be another powerful kaiju. Maybe a new, mysterious kaiju that was introduced into the Monsterverse secretly. This new kaiju could have some special abilities that were passed on to King Ghidorah's offspring.
One possible plot could be about how the other kaiju react to King Ghidorah's pregnancy. Maybe Godzilla would be initially shocked and then start to consider if this new situation changes the power balance among them.
There are some Tumblr blogs that focus on kaiju fanfiction. You could search for tags related to Female King Ghidorah on Tumblr. Also, don't forget to check out Wattpad. Although it has a broader range of content, you may be able to find some unique takes on Female King Ghidorah in the form of fanfiction there.