While the Titans ruled, the Flame resided in Kronos' castle. A wild young thing, she delighted in the antics of the Titans. She was young and burned brightly, as all fire does at first. She was also rather naive and unaware of the ways of the world.
When Hestia was first born, Kronos introduced the Flame to his eldest daughter. He had been so excited about her birth that, for a short time at least, he had completely forgotten his father's doomed prophecy. Still, it came back to haunt him the instant his daughter reached out her chubby little fingers and the Flame reached back. In that moment, Kronos realized that his daughter, his adorably cute and wonderful little daughter, was secretly a menace. She was no Titan. She was a goddess, a more powerful deity, and one day she was going to rise to destroy him. It took Kronos a few guilt-ridden hours to summon up the courage, but when he did, he swallowed her whole.
A few centuries later, when Zeus cast his lightning bolt and toppled Kronos from his throne, his siblings stormed the tower alongside him. Her siblings were intent on defeating the Titans living there, but Hestia went to find the room that housed one of her oldest and fondest memories. And find it she did.
After many hours and even more wrong turns, she'd finally returned. Returned to the room of the young godlike entity that flickered and glowed and constantly changed forms. Instead of charging or attacking like one of her siblings, Hestia called out to the child.
The Flame turned, as if curious. As if something about Hestia called to it.
"Hello? Who are you?"
The Flame was young and strayed from that which seemed too new, but the goddess in front of her was familiar. The Flame did not shy away.
"My name is Hestia," Hestia told the little girl. "What's your name?"
The little girl turned and winced.
'I don't know,' the Flame seemed to say.
"That's alright," Hestia told her, reaching out a hand. "You don't need to know yet. Would you like to come with me? I can keep you safe."
Just like centuries ago, the Flame reached back. In one fateful instant, Hestia claimed the Eternal Flame for Olympus. For her home. For her family.