The Golden Magikarp, also known as the more simple 'Shiny Magikarp' is like any other shiny Pokemon - meaning that the chance of a Shiny Magikarp's offspring being shiny is still the dumb old 1 in 8,000 chance.
However, unless you use all possible methods to increase your chances of getting a shiny (I'll list them when I find them. xD) the lowest chance of finding a shiny through an egg is 1 in 1,000. That's eight times the luck.
But, since a Pokemon is shiny doesn't mean that it's offspring will be shiny (or, will have an advantage of being shiny). Sorry. :(
Hope I helped. :)
Source: My wonderful self.
EDIT: To reach a 1 in 1,000 chance you will need to do the Masuda Method (breed two Pokemon that are from different countries, like an American Magikarp and a German Poliwhirl or something - this increases your chances to 3 in 4,096 (around 1 in 1,365 with a bunch of decimal places after)
The Shiny Charm which can be acquired by showing your completed Unova Pokedex to Cedric Juniper - he will give you the Shiny Charm which would increase your chances to 1 in 2,730. When you acquire this, you will always have this, meaning it will always be 1 in 2,730 and not 1 in 8,192.
Combining these two methods together creates the chance of a 1 in 1,024 chance to get a shiny egg. Eight times better the chance than normal.
There you go! Hope I helped. :)