Is there any validated measurements of game experience (e.g. focusing on flow, presence, engagement, etc..) for children or young people?

You’re welcome.

Thanks for your advice!

MDA and DPE frameworks may be helpful to you on this issue, as they talk about the game design based on user experience. But I think you have to decide what to use as a metrics because both papers talk about how to connect game design to user experience, they do not tell about the metrics systems they used in the projects.