Yes, it is possible to hatch a shiny even if one of the parents is Ditto, it is no different than breeding with other Pokémon, the chance will still be 1/4096.
If you mean will having a shiny Ditto as one of the parents increase the shiny rate, then no, as having shiny parents do not affect the chance if hatching a shiny Pokémon.
Mention that if Ditto is of a different region from the other Pokémon, shiny chances are increased btw
commented 1 minute ago by Fated Fathom ♠
Thank you Qwerty for pointing that out. Indeed, if your parents are of differing country origins, then your chances of hatching a shiny is increased.
So for example, if you have a Japanese Ditto and breed it with an American Charmander, then the chances of hatching a shiny are increased. This is why many people want a foreign Ditto, as it is compatible with any breedable Pokémon.
This method is called the Masuda Method.
Source: Experience
