Well you get more chances since you will hatch more eggs but it doesnt boost your chance of getting one, using the shiny charm helps alot.
best way is the madasuda method
>The Masuda method (Japanese: 国際結婚 international marriage), also known as Masuda's method, is a fan-made term which describes a way to obtain Shiny Pokémon more easily from Generation IV onwards. While the standard encounter rate for a Shiny Pokémon (either in the wild or by breeding) is 1/8192, the Masuda method multiplies this rate by 5 (to 5/8192 or about 1/1638) in Generation IV and by 6 (to 3/4096 or about 1/1365) in Generation V. It occurs whenever Pokémon of differing real-world geographical origin are bred.
These are you chances with madsuda method but with shiny charm you have even a better chance, trust me its worth to "catch em all". I can even help you with that :D
your chances with masuda method
1/1024 or 1/512 with the Shiny Charm.
This can help you