The shiny encounter rate was thought to be 1/8192, just like in the regular games, which comes out to 0.012%. With donator status, it was thought to be 1/7373, which would be 0.014% (rounded up).
There's no way that 0.012% pops up here as a coincidence. If nothing else, it was just the developers making a subtle joke. Though, I think it's outdated, as 1/8192 no longer seems to be the rate.