Whenever you get a Pokémon come to you after cooking a meal, there is a chance for it to be Shiny. All Pokémon can be Shiny giving you strong chances to get them.

There are no standard ways for you to improve the odds for a Shiny Pokémon but as standard, it's a 1 in 4096 chance for a Pokémon to be shiny, but due to how Pokémon Quest works, you will have 81 rolls at the chance

If the value matches, then you will get a Shiny Pokémon. This means that you effectively have a 1 in 51.06 chance of getting a Shiny Pokémon with each Pokémon summoned.