1/512.
The only factors affecting the shiny odds in what you laid out are the Masuda Method and the Shiny charm. The shininess of the parent only affects the shiny odds in Gen 2 (I'm 88% percent sure it's only Gen 2, please correct me if I'm wrong), and Sparkling Power has no affect on eggs whatsoever.
Although it doesn't increase the shiny odds, you can use Egg Power to get more eggs faster, and both Egg Power and the abilities Flame Body, Magma Armor, and Steam Engine speed up the hatching time of eggs.
Source: Experience.
Hope I helped!