It's the same as any regular Pokemon. A 1/8192 chance. To obtain one will require a: luck, b: a lot of effort, or c: hacking.
A: maybe you'll get lucky and receive a shiny starter, or find someone willing to trade you one.
B: You could breed starter Pokemon until you hatch a shiny one (it is recommended you use the Musada method when doing this)
C: Hack, or use one of the Pokemon creation websites or apps, such as pokegen or Pokebuilder
Hope this helps