Main Series
Gen 1: 1/8192, N/A
Gen 2: 1/8192
Gen 3: 1/8192
Gen 4: 1/8192
Gen 5: 1/8192
Gen 6: 1/4096
Gen 7: 1/4096
Gen 8: 1/4096
Boosted Odds:
Gen 1: N/A
Gen 2: Breeding a Shiny Pokémon if the offspring is the opposite gender (1/64)
Gen 3:
Gen 4: Masuda Method (5/8192), Cute Charm Glitch (1/24576 – 21.34%), Poke Radar chaining (single patch): ≥40 (41/8192)
Gen 5: Masuda Method (6/8192), Shiny Charm(+2/8192)
Gen 6: Masuda Method (6/4096), Poke Radar chaining (single patch): ≥40 (1/100), Shiny Charm (+2/4096), Friend Safari (5/4096), Fish Chaining (41/4096), Hidden Pokémon: Search Level 200 + X (0.08% + X*0.01%)
Gen 7: Masuda Method (6/4096), Shiny Charm (+2/4096), SOS Battles: ≥31 (13/4096)
Gen 8: Masuda Method (6/4096), Shiny Charm (+2/4096), Dynamax Adventure (1/300)
Spin off series:
Rumble:
In Pokémon Rumble, Shiny Pokémon may rarely appear. They will always tip over when defeated. The chances of their appearance are unconfirmed, although they appear to occur more often than in the core series.
Pokémon Rumble U
Shiny Pokémon return to the Pokémon Rumble series in Pokémon Rumble U though are only obtainable through the use of passwords or the NFC Rumble U Figures.
Pokémon Mystery Dungeon: Explorers of Time, Darkness and Sky:
In Pokémon Mystery Dungeon: Explorers of Time and Explorers of Darkness and Explorers of Sky, a Shiny Celebi is part of the story, although Shiny Pokémon are not obtainable normally in the game.
Pokémon Mystery Dungeon WiiWare
In the Pokémon Mystery Dungeon games for WiiWare, Shiny Pokémon can be found in dungeons. Unlike the core series, only 36 different species of Shiny Pokémon are obtainable. The chances of finding one in a dungeon is the same as finding one in the wild in the core series.
Pokémon Mystery Dungeon: Gates to Infinity
In Pokémon Mystery Dungeon: Gates to Infinity, Ho-Oh can be uniquely encountered as a Shiny Pokémon at Eternal Ruins through a Legend of the Mysterious Ruins job request. This Shiny Ho-Oh has a slightly different moveset to the regular Ho-Oh that can be met. It also has a unique animation that plays before the battle begins
Pokémon Super Mystery Dungeon
> The Shiny Celebi from Pokémon Mystery Dungeon: Explorers of Time, Darkness, and Sky makes an appearance.
Pokémon Mystery Dungeon: Rescue Team DX
27 Mystery Dungeons, once completed for the first time, will have "Strong Foe" Pokémon that spawn. These Pokémon have a higher than normal chance of being Shiny compared to the main series. Shiny Pokémon cannot be recruited unless the Player has the Friend Bow equipped and the Shiny Pokémon's respective Camp purchased. Recruitment is still not guaranteed if these criteria are met.
The exact odds are unknown.
Pokémon Conquest
A Shiny Rayquaza is featured in Pokémon Conquest, sharing a Perfect Link with Nobunaga, and is his Pokémon of choice during the final battle of the main scenario. Nobunaga's Black Rayquaza was distributed over Wi-Fi for Japanese Black and White players to commemorate the release of the game.
Pokemon Shuffle
17 Shinies available, but they're static.
Pokémon GO
In Pokémon GO, certain Pokémon species have a chance of being Shiny, with each species having its own Shiny rate. For most Pokémon, the Shiny rate is approximately 1 in 450. However, in certain in-game events, the Shiny chance may be increased for certain Pokémon. For example, on Community Days, the featured Pokémon will always have increased Shiny odds. Shiny Pokémon may be encountered through any method: randomly in the wild, from hatching Eggs, by completing Field Research tasks, by winning Raid Battles, or as GO Battle League rewards. All Pokémon seen in the overworld appear non-Shiny, but when a player attempts to capture a Pokémon, it may appear as a Shiny Pokémon. Likewise, during a Raid Battle, the Raid Boss always appears non-Shiny during battle, but it may become Shiny during the bonus challenge. Shiny encounters are random for each player, meaning that if two players attempt to catch the same Pokémon, one player may encounter a Shiny Pokémon and the other may not.
Pokemon Quest
Pokémon can appear Shiny in Pokémon Quest. When viewing the Pokémon's details, the Pokémon's picture will appear in its shiny coloration. The only benefit to having a Shiny Pokémon in Pokémon Quest is to gain 20 PM Tickets. Otherwise, it is just an aesthetic feature. It is considered that there is a 1/75 to a 1/100 chance of attracting one
Pokemon Masters Ex
Presumed to be ~1%
Source, Source
