Perhaps he could use his phoenix form to travel to places that are otherwise inaccessible. He could fly to the Forbidden Forest's most secret corners and discover new magical creatures or ancient magic. Also, his rebirth as a phoenix might give him the power to communicate with other phoenixes, and they could pass on their ancient wisdom to him.
Well, a great plot in harry potter and phoenix fanfiction could be about the Marauders' Map falling into the wrong hands. This could lead to a whole new set of adventures and dangers for Harry and his friends. Also, fanfiction could explore the backstories of some of the minor characters in the Order of the Phoenix. What if one of them had a hidden connection to Voldemort's past? It would add a new layer of mystery and intrigue to the story.
One idea could be being reborn as Harry's long - lost twin. You could then have a whole new dynamic where you both share the burden of being the Boy Who Lived, but also have your own unique abilities and personalities. Another plot could be being reborn as a Slytherin who tries to change the house's reputation from the inside. You might start off being shunned by the other Gryffindors and friends of Harry, but slowly prove that not all Slytherins are bad.
One interesting plot could be a character reborn with memories of the future. For example, a minor character who remembers Voldemort's rise and fall and tries to change things in a different way. They might try to prevent certain deaths or change the course of the wizarding wars.
In some fanfictions, a plot idea is to have Harry gain a new power. In the context of 'Harry Potter Order of the Phoenix', it could be a power related to his connection with the late Sirius Black. For instance, he might be able to communicate with Sirius in a new way, like through dreams more vividly. This could change the way he approaches his fight against Voldemort and the Death Eaters. Also, a plot could involve the Ministry of Magic having a more complex internal struggle that affects the Order's operations.
In a fanfiction, the Phoenix and the Basilisk could be two parts of an ancient prophecy. Harry Potter is the one foretold to either unite them or destroy one to save the other. Along the way, he has to learn about the true nature of both creatures. He might find that the Basilisk isn't as purely evil as it seems and the Phoenix has a more complex role than just being a symbol of good. This could lead to a very engaging story full of moral dilemmas and exciting magical encounters.
A plot could be where the Phoenix wand is stolen and Harry has to go on a quest to get it back. He might have to face dark wizards who want to use the power of the phoenix feather for evil. Along the way, he discovers more about the true nature of his wand and the connection it has to the wizarding world as a whole.
Well, a plot might involve Harry - now James - trying to change the fate of his family. He could focus on protecting Lily in a different way than James did in the original story. Maybe he'd use his knowledge of magic from his past life to create new spells or defenses. Also, his relationship with Snape could be very different. Since he was Harry before, he might understand Snape's feelings better and try to make amends or change the animosity between them.
In this fanfiction concept, it might be interesting if Harry, as a Targaryen, is born with the ability to communicate with dragons in a more profound way than the typical Targaryen. This could be because of his past life experiences with magical creatures. He could use this connection to his advantage, uniting the different factions in Westeros. Also, his memories of the Sorting Hat might influence how he views the different houses or families in Westeros, and he could strive to create a more inclusive society.
One idea could be that Harry is reborn into the world of 'Reborn' with his magical abilities intact. He could use magic to solve the mysteries and challenges in the 'Reborn' world, like helping Tsuna in a unique way. Another plot could involve the magic of the 'Harry Potter' universe somehow getting intertwined with the flames in 'Reborn'.
One idea could be being reborn as a muggle - born wizard who has a unique ability to communicate with magical creatures in ways others can't. This could lead to all sorts of adventures in the Forbidden Forest and uncovering secrets about the creatures that help in the fight against Voldemort.