No the chance to see any shiny pokemon is 1/8192 no matter what pokemon it is. A shiny pokemon has the same catch rate as its normal color form. All genrations have the same chance of seeing a shiny pokemon (1/8192), it starts in generation 2( credit to Shadow Lucario) you can use Masuda Method(Credit to Zekrom-Sammy) by breeding two pokemon from different contries that will increase you chance of the pokemon from the egg to be shiny.