Shiny Chance

No Shiny Charm:
1/8192 chance of getting a shiny on a Route

1/4096 chance of getting a shiny in a Dungeon

1/2048 chance of getting a shiny from a Evolution stone/item

1/2048 chance of getting a shiny from a Shop

1/2048 chance of getting a shiny from the Safari Zone

1/1024 chance of getting a shiny on an Egg

Level 5: Shiny Charm:
1/4096 chance of getting a shiny on a Route

1/2048 chance of getting a shiny in a Dungeon

1/2048 chance of getting a shiny from a Evolution stone/item

1/1024 chance of getting a shiny from a Shop

1/1024 chance of getting a shiny from the Safari Zone

1/512 chance of getting a shiny on an Egg

Trivia
Shinies as over Version 0.3.0 now increase click damage at a 50% rate compared to normal Pokémon.