Likely none.
Judging by the game's website
Harry Potter: Hogwarts Mystery is the first game in which players can create their own character and experience life as a Hogwarts student. The game will launch under Portkey Games, from Warner Bros. Interactive Entertainment, the games label dedicated to creating new Wizarding World mobile and video game experiences that place the player at the centre of their own adventure, inspired by J.K. Rowling’s original stories.
and the press release on Pottermore
The game has been created by Los Angeles-based mobile games studio Jam City, and will be part of the Portkey Games label from Warner Bros. Interactive Entertainment – you can read more about Portkey here.
‘As Harry Potter fanatics ourselves, we have great respect for the millions of people throughout the world who have followed the Harry Potter stories for more than 20 years,’ says Chris DeWolfe, co-founder and CEO of Jam City. ‘This game is a labour of love for our developers and artists, who are dedicated to creating the most magical entertainment and game play experience for everyone who adores J.K. Rowling’s Wizarding World.’
and the press release on Portkey Games
As well as the familiar, you’ll also be able to visit new locations and explore new story elements, again, all inspired by the wizarding world.
David Haddad, President of Warner Bros. Interactive Entertainment, says he is ‘thrilled’ by the new launch, and the games to come.
‘With Portkey Games, we are thrilled to answer the fans’ requests for more games inspired by J.K. Rowling’s Wizarding World,’ he says. ‘We are working with talented creators to build games that focus on player-generated stories, which will live alongside the magical universe created by J.K. Rowling.’
Everything seems to be "inspired" by the Wizarding World. There is no mention of direct involvement from J. K. Rowling herself.