The Shiny Charm increases the chance of encountering a Shiny Pokémon, both in the wild (including static encounters, such as Legendary Pokémon[1]) and via breeding. This is done by generating two extra personality values to attempt to find one that is Shiny, effectively resulting in a tripled chance to find Shiny Pokémon compared to the base chance; from 1/8192 to approximately 3/8192 (roughly 1/2731). This stacks with most other modifiers which increase the Shiny encounter rate, such as the Masuda method. It has no effect on Pokémon obtained via NPCs from in-game trades, gifts, or from Event Pokémon obtained via Mystery Gift.
Generation VI to VII
Starting in Generation VI, the base encounter rate for Shiny Pokémon was increased from 1/8192 to 1/4096. As such, the Shiny Charm's two extra rerolls now increase the chance of encountering a Shiny Pokémon from 1/4096 to approximately 3/4096 (roughly 1/1365).
Due to a bug, when breeding, if any personality value rerolls are applied, (such as the additional shiny rolls provided via the Masuda method or Shiny Charm), the initial roll to generate a personality value is skipped.[3][4]
The result is that when breeding using the Shiny Charm alone, it only provides 2 total rolls for the personality value, meaning there is approximately a 2/4096 (equal to 1/2048) chance of hatching a Shiny Pokémon. This is a reduction from prior generations where the initial roll and both rerolls are accounted for, which would provide a shiny rate of 3/4096, (approximately 1/1365).
However, in Generation VIII, due to the Masuda method providing one more reroll than in previous generations, the chance of hatching a Shiny Pokémon when using both the Shiny Charm and Masuda method is unchanged, providing 8 total rolls, (instead of the intended 9), for a Shiny rate of 8/4096 (equal to 1/512) as usual (instead of the intended 9/4096 (equal to 1/455)).
In Dynamax Adventures, Pokémon normally have a 1/300 chance of being Shiny, (this is determined at the end of the activity where you select a Pokémon to keep from the 4 encounters, rather than when the Pokémon is encountered during the activity, as all Pokémon appear non-Shiny during a Dynamax Adventure). With the Shiny Charm, this chance is changed to exactly 3/300, (effectively 1/100).[5]
Despite the Shiny Charm only having an effect on the chances of obtaining a Shiny Pokémon via breeding in Pokémon Brilliant Diamond and Shining Pearl, the item description erroneously states that it will "increase the chance of finding a Shiny Pokémon in the wild".
This text is identical to prior games, (excluding Generation V), and the internal code explicitly disables the Shiny Charm for other encounter types. This heavily implies the item is functioning as intended, with the item description having been copied verbatim being a developer oversight.