It could be a symbol of Gryffindor's spirit in the fanfic. When Harry wields the flame, he is representing all the brave and noble qualities of the Gryffindor house, and it might inspire others around him to be braver too. Also, the flame might have some special abilities like being able to break dark spells or protect the innocent.
Maybe he stumbles upon it during a time of great danger in the fanfic. For example, when facing a powerful dark wizard, he might feel an unusual warmth and strength within him, and then realizes it's the power of the Gryffindor flame.
It could be a key to unlocking hidden secrets within the Gryffindor house. For example, there might be a secret chamber that only the one who can control the flame can access, and inside there are powerful spells or artifacts.
Maybe it has something to do with Harry's exploration of his own heritage. As he delves deeper into the history of Gryffindor and his own family's connection to the founder. He comes across an old spell or an enchanted object that, when he touches it, he feels a strange power flowing through him. This power then manifests as the ability to control the flame of Gryffindor.
One great fanfic could be 'The Gryffindor's Legacy' where Harry's holding of the flame is a central plot point for him to unlock ancient Gryffindor powers. Another might be 'Flamebearer Harry' which focuses on how he uses the flame to inspire the other Gryffindors in difficult times. There could also be 'Harry and the Flame's Purpose' where he discovers the true meaning of the Gryffindor flame through a series of adventures.
Well, fanfiction.net is a great place to start. Just use their search function and type in 'Harry holds the flame of Gryffindor'. You might have to sift through some results, but you should be able to find relevant fanfics. AO3 is also really good. They have a tagging system, so if you search for tags like 'Harry Potter', 'Gryffindor', and 'flame', you'll likely come across the fanfics you're looking for. Additionally, some smaller Harry Potter - focused fanfic websites might also have such stories, but they may not be as well - organized as the big two.
Perhaps Harry has his own vision of Gryffindor and the fanfics he's seen don't align with it. He might have a deep - seated understanding of what Gryffindor means to him, like courage, loyalty, and friendship in a very personal way. The fanfics, on the other hand, might focus on more superficial or inappropriate aspects of Gryffindor for his taste, such as focusing too much on power plays or false bravado rather than the true essence of what makes Gryffindor great.
A RWBY character with the Sword of Gryffindor might also experience a change in their personality or outlook. Since the sword is associated with Gryffindor values, the character could become more courageous and noble. They might also start to uphold values that are more in line with the Harry Potter universe, which could create an interesting dynamic within the RWBY world.
Well, Gryffindor could protect Harry by being there for him emotionally. In the fanfiction, Gryffindors might offer him a safe place to talk and share his troubles. They would encourage him when he feels down or doubts himself. Also, Gryffindor as a whole House could provide Harry with resources, like access to certain magical knowledge or artifacts within the Gryffindor common room that can help him in his battles against the dark forces.
In some fanfics, Harry might be made to hate Gryffindor perhaps because the author wants to explore an alternative personality for him. Maybe they want to show how the Gryffindor house's values, like bravado or recklessness, could be seen in a negative light from Harry's perspective.
It might make some Gryffindor fans in the fanfiction world feel disappointed. They may have hoped for his approval or participation in some way.