The story would change significantly. Harry would have access to Dumbledore's vast knowledge and experiences. He might learn about different magical theories and practices that Dumbledore had encountered over the years. This could give Harry an edge in battles or in solving mysteries within the wizarding world.
In some fanfictions, when Harry gets Dumbledore's memories, he might find out about alternative plans Dumbledore had for him. Maybe there were backup strategies to defeat Voldemort that no one else knew about. Harry could then use this knowledge to train his friends in new ways or to strengthen the defenses of Hogwarts in ways that were previously unimagined. This often leads to a more powerful and self - assured Harry in the fanfiction world.
There may be such extremely non - canon and inappropriate fanfiction out there in the vastness of the internet, but it goes against the original nature and values of the Harry Potter series. J.K. Rowling's world has certain boundaries and this concept is far from what was intended in the original story.
The main problem is that it's completely against the canon. Dumbledore is a much older and mentor - like figure to Harry, and the idea of such a relationship is inappropriate and goes against the moral and ethical framework of the original story.
Hermione would be a likely supporter. She is always loyal to Harry and if he presented her with evidence of Dumbledore's wrongdoings, she would probably side with him. She has the intelligence to help Harry strategize and find ways to expose Dumbledore. For example, she could use her research skills to dig deeper into Dumbledore's past.
There's also a chance that Dumbledore gets caught by a group of rogue magical creatures. For instance, if he was exploring an area that was supposed to be off - limits to wizards and the creatures there saw him as an intruder. They might not be as rational as wizards and could hold him captive without really understanding who he is.
Well, Harry would probably have a very different upbringing. He'd be surrounded by Dumbledore's wisdom all the time. He might learn magic at a much faster pace and gain deeper insights into the wizarding world's history and secrets right from the start. Dumbledore could also protect him more effectively from the dark forces, as he's one of the most powerful wizards. And Harry would grow up in an environment full of magic and knowledge, which would shape him into a different kind of wizard compared to the original story.
In a 'Harry Potter gets revenge on Dumbledore' fanfiction, Harry could find out that Dumbledore knew about certain threats to his life but didn't do enough to protect him. So, Harry decides to get revenge by undermining Dumbledore's influence at Hogwarts. He might start by convincing the other students that Dumbledore isn't as infallible as they thought. He could do this by revealing some of Dumbledore's past mistakes. Then, he could work on getting the school governors to question Dumbledore's leadership, gradually chipping away at his power and status within the wizarding community.
His friends like Ron and Hermione could be his allies. They have always stood by Harry and if Harry believes that Dumbledore has wronged him, they might side with him. Ron, with his loyalty and Hermione with her intelligence could help Harry plan and execute his revenge. They could use their knowledge of magic and Hogwarts to find ways to undermine Dumbledore's influence.
It could be Severus Snape. He has a complex relationship with Dumbledore. Maybe Snape discovers some of Dumbledore's plans that he doesn't agree with regarding Harry Potter. He then sends a Howler in a fit of anger to express his disapproval.