I am in the room with the Xerneas tree, and I keep reopening the game to find a shiny. Is it possible to find a shiny that way? If so, than will it show Xerneas shiny in the cutscene?
No, this is not possible. Starting with Generation 5, some Pokemon are programmed such that you cannot encounter their shiny variant in the wild.
Taken directly from Bulbapedia:
Unobtainable Shiny Pokémon
In all generations since Shiny Pokémon debuted, there are a few species that cannot be legitimately obtained Shiny. This can be caused by being impossible to obtain except through a direct event distribution, or by being programmed so that they cannot be Shiny in the wild (Generation V onward).
- Mew[note 1]
Generation III and on
Generation IV and on
- Spiky-eared Pichu*
Generation V and on