PokéBase - Pokémon Q&A
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The answers are outdated, so I'll give you an updated answer!

The short answer, like the other said, is no. There is no guarentee of a shiny offspring from two parents.

In Gen 5 and earlier, the shiny odds were 1/8192, and since Gen 6, the odds have been halved to about 1/4000.

There's other ways to manipulate your odds on shininess, such as the Masuda Method (introduced Gen 4) and using the shiny charm (introduced Gen 5). Both of those still exist to current day (Gen 8).

In Gen 2, breeding shiny parents together could impact the odds of the offspring being shiny, since the shininess was determined by IV's. That is also why some Gen 1 Pokemon could result in being shiny when transferred from RBY to GSC--it was IV based. However, breeding trick was only in Gen 2, and it's still not guaranteed.

Souce: knowledge, experience. I'll add sources if anyone doubts this :P

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Lmao TY. This question is 8 years old.
Yeah, that's the point to the *updated answer*
You're allowed to answer an old question if the other answers are wrong or outdated. Read Ty's first sentence.
3 votes

What charizard said is true, breeding shiny Pokemon is just like breeding regular Pokemon, the shiny chance never changes from 1/8192. However, if one of the parent pokemon is originally from a foreign game, the chance of shininess in the baby newly hatched pokemon is drastically increased, this is known as the mesuda method.

Starting in BW2, the shiny charm also increases the shiny chance.
1 vote

Not necessarily because the egg still has a 1/8192 chance of being shiny. The only thing the parents effect in the offspring are the IVs, stats it is born with, and the type of pokemon it is.