Let's take the case where two players would face the same Pokémon on the map. The first player would launch the battle, and find out that the opposite Pokémon is shiny.
If the second player launch the encounter with the same Pokémon, will the Pokémon also be shiny for him?
Bad luck, it seems that the second player won't get a shiny Pokémon, except if he is really lucky too.
Silph Road's Reddit users which were playing together confirmed that, while launching the encounter against the same Magikarp, only one of the two players faced a shiny Magikarp.
Another user confirmed it in the comments too:
I have a shiny magikarp, my girlfriend and I are both level 24. The magikarp she caught was not shiny.
