In this demo, Professor Oak meets you in Viridian Forest and suggests you do some research in the forest. The forest contains different Pokémon to how they are in the game itself. This demo is not compatible with Pokémon Let's Go, Pikachu! or Let's Go, Eevee! so all Pokémon and items obtained within the demo are not saved. Shiny Pokémon can be found in the demo.
As the demo is not compatible with the actual games, there is no way to move the shinies out of the demo, unfortunately.
Hope I helped!