I'm putting this first part as an answer because it would be too long of a comment.
In response to your two questions in the comments:
For breeding a shiny you need a Pokemon (normally a Ditto) from a different country to breed with a Pokemon whose offspring would be the species of the Pokemon you want to be shiny. Breeding a Pokemon with one from a different country raises the likelihood of it being shiny (but you still need patience), this is called the Masuda Method. The Masuda Method raises you chances of finding a shiny from 1/8192 to 5/8192.
It will be difficult to get a Pokemon from a different country in Gen 5 games because the GTS is shut down. If you wish to pursue this method I suggest asking on Bulbagarden trade forums, it's probably your best chance.
The shiny charm is an item introduced in Black 2/White 2 that raises the likelihood of finding a shiny from 1/8192 to 3/8192. Having the shiny charm and using the Masuda Method therefor raises your chances of finding a shiny from 1/8192 to 8/8192. The shiny charm is a key item and cannot be traded from game to game, to get it in B2/W2 you need to catch every single Pokemon in the national pokedex (excluding mythicals) and then have your pokedex evaluated by Cedric Juniper before talking to Professor Juniper in Nuvema town.
Now, as for Sun.
First of all, after Gen 5 the chances of encountering a shiny Pokemon were raised from 1/8192 to 1/4096. For a complete guide on finding shiny Pokemon in Sun and Mood I would like to direct you to this link, which explains the SOS method as well as older methods such as the Masuda Method and soft-resetting, it also tells you about the shiny charm in these games.