Kai was not born as Malachai Montgomery. He was intended to be named Ethan, and was the son of a young couple, Brent and Margarette Walsh, who were both half-blood wizards. Both were Aurors, and died in action, effectively orphaning the young Ethan, who was then adopted by Melisandre Montgomery - one of Margarette's closest friends from Ilvermorny in the United States. He was only a few days old when he was adopted, and was not yet given a birth certificate, so Melisandre decided to name him Malachai instead, unaware that his parents wanted him to be called Ethan.
He grew up in a large house near the Atlanta, Georgia area, along with his adoptive siblings, Elesa, Beau and Corbin who are all biological children of Melisandre and her husband, Thorthon. Malachai is the youngest of the bunch, and was never told that he was adopted. He figured it out, though, as he grew up, having noticed that he never gets as much attention as his other siblings do. He did his own investigation, and arrived to that conclusion. Because of that, he would always strive to make other people like him, instead.
He showed his first sign of magic at age 10, when he was able to make the silverware float during a family reunion dinner. After that, he was admitted to Ilvermorny, where the rest of his siblings already go to, and was sorted to Wampus. His natural good looks and charm made him popular, and soon enough, his entry into his House's quidditch team on just his first year boosted that as well. He gained more popularity as the years went by, and grew more cocky and confident as well. He started caring too much about his reputation, that he lost his already diminishing touch with his family. It's not as if they care though, because he had already long accepted that in their household, they all operate under the mantra: 'to each his own.'
As the years passed, his Quidditch career at school flourished, and he got into some other new things as well. He developed a passion for duelling, and even some muggle sports that was taught to him by his muggle-born friends like basketball, volleyball, and weightlifting. He also became rather adventurous, often going out with his friends to hike mountains, and go to muggle themed parks and other places across continental America. Before he entered his sixth year, he heard of this student exchange program which would give students the chance to be sent to Hogwarts in the UK. Raring to start and adventure in Europe (and to get away from his family, even for just a bit), Kai signed up and was ecstatic to be accepted.