Yes, there might be. The Game of Thrones fandom is vast, and many creative fanfics exist. You can start by looking on popular fanfic websites like Archive of Our Own or FanFiction.net.
Perhaps the OC son has a special ability or gift that Jon Arryn was trying to protect him from being exploited for. After Jon Arryn's death, the son has to learn to control this ability while also dealing with the power struggles in King's Landing. He could be a key figure in the fight against the White Walkers, using his unique skills to help the living, all while trying to uphold his father's legacy.
Well, he could be a character who has been reimagined. Jon Arryn in the original series was an important figure. In this fanfic, the 'Brightflame' addition might suggest some sort of connection to a more flamboyant or perhaps magically - inclined lineage. It's possible that he has abilities or a backstory that ties him to this 'Brightflame' concept, which could make him a key player in the fanfic's plot, different from his role in the original story.
The concept of heir in a 'Game of Thrones' fanfic involving Jon Arryn and Brightflame is highly variable. There are so many factors at play. The world of 'Game of Thrones' is full of complex family trees and political relationships. It's possible that an heir could emerge from a previously unthought - of branch of the family. Maybe there's a secret marriage in the past that ties a character to both Jon Arryn and Brightflame in a way that gives them a legitimate claim to be the heir. And then there are the power - hungry lords and ladies who might try to manipulate the situation to their advantage, putting forward their own candidates as the heir, whether they have a real claim or not.
The 'Game of Thrones' world is vast and full of possibilities in fanfiction. Regarding Jon Arryn's wife in a Blackfyre - related fanfic, it's likely that the fanfic author has crafted a unique story. It could be that the wife is a character who is a part of a secret Blackfyre plot, or she might be a noblewoman from a house that has some connection to the Blackfyre legacy. However, without actually delving into the fanfic, we can only speculate about who she might be.
One idea could be that this adult son might have been involved in the political intrigue in King's Landing. He could have been a rival to Littlefinger, using his father's influence and his own wits to try and maintain the stability of the realm. Maybe he would have uncovered some of Littlefinger's schemes earlier, preventing some of the chaos that ensued in the series.
The plot could involve a time - travel or alternate universe scenario. Maybe Blackfyre is brought to the present time in the Game of Thrones story (or an alternate version of it), and Jon Arryn marries her out of love. Their relationship then has to face the challenges of the existing power structures, the plots of other houses, and the secrets that Blackfyre might carry from her own past. This could lead to a whole new set of alliances and enmities within the Seven Kingdoms.
The OC son could start off as a naive and sheltered young man, but after Jon Arryn's death, he is forced to grow up quickly. He becomes more cynical and distrustful of those around him, especially the nobles in King's Landing.
In the fanfic, she could be a key figure in a political plot. Maybe she has some connection to the Blackfyre claims which could influence the power dynamics in the story.
He could be a central figure driving the plot. For example, if his 'Brightflame' aspect gives him some special power, he might be using it to influence the political or magical landscape in the fanfic's version of Westeros.