One possible plot could be that the dragon is from another dimension and has some sort of connection to Michelle Jones. Strange, being the Sorcerer Supreme, senses this and tries to figure out how it all fits together. The fanfic could show how Michelle Jones adapts to this new and strange (no pun intended) situation, and how her character develops throughout the story as she gets involved with the dragon and Strange's world of magic.
In a fanfic like this, the relationship between the characters can be explored in various ways. For example, the dragon might be a key to unlocking some hidden power within Michelle Jones. And Strange, with his vast knowledge of the mystic arts, could be guiding her through this new discovery. The fanfic could be set in the chaotic and magical world of the MCU, with different dimensions and spells playing a major role.
There could be many interesting fanfics involving these characters. Maybe it's a story where Michelle Jones discovers a magical dragon while Dr. Strange is trying to keep the magical world in balance. She could end up helping Strange in his adventures with the dragon's unique powers.