Perhaps the start of the fanfic could be that Voldemort's final curse on Harry backfires in a strange way due to some ancient magic. Instead of just leaving a scar, it sends Harry through a portal to Panem. He lands in the Capitol, where he's immediately seen as an oddity. But before the Capitol can fully study him, he manages to escape and finds himself in a district. There, he begins his journey of growing up in Panem, with his wizarding skills gradually emerging as he faces the hardships of this new world.
It could be really interesting. Harry would face a whole new set of challenges in Panem. Instead of Hogwarts, he might attend the Capitol's training schools. His magic could be a huge advantage or a target in the Hunger Games - like world of Panem. He'd also have to deal with the political intrigue and power struggles there, which are very different from the wizarding world he was originally from.
It could start with Harry being found as a baby in Rome. Maybe a Roman wizard family takes him in. They notice his special powers right away and start to train him in their ways.
Most likely very negatively. The Harry Potter fan community values the positive aspects of the series. They would see this fanfic as a disrespect to the original work and its characters.
He'd be more disciplined. His character would be shaped by military values. He'd be less likely to act impulsively and more likely to think things through strategically.
He'd be tougher. Hiei's no - nonsense attitude would rub off on him. Harry would be more likely to take risks without hesitation.
Harry's character would be more attuned to the deeper magics. He would be less likely to jump into things without thinking. Since Flamel is a master of alchemy, Harry might be more interested in the scientific aspects of magic. He would also have a greater respect for life and magic's power, as Flamel, with his long life, would instill in Harry a sense of wonder and caution about the forces they deal with.
It could start with Harry being found by a Hetalia - inspired character or family. Maybe he's discovered in an alley in a world where Hetalia and Harry Potter elements co - exist, and this new family decides to raise him.
Harry Potter's character would likely develop a stronger sense of independence. Since Jack Frost is often portrayed as a solitary figure, Harry might learn to rely on himself more. He could also develop a sense of wonder for the natural elements, especially ice and snow. His values might shift towards a more elemental view of magic, and he might be less interested in the politics and social hierarchy within the wizarding world. His sense of justice could still be strong, but it would be more in line with the unyielding nature of ice, being very firm and unwavering.
His character would become more rugged. Instead of the somewhat sheltered and naive Harry we see at the start of the original series, he'd be tough - minded. Burt Gummer's influence would make him more of a fighter from the get - go.
It could start with Harry Potter having a vision of a perfect city. He wakes up one day with this idea in his head and decides to set out on the journey of creating it. He starts by finding a suitable piece of land, perhaps an abandoned area that he can transform with magic.