So called "shiny Pokemon" only exist in the main games, and the original Rumble. The only "shinies" you'll find in here are ones also known as "sparkling," which mean they've got a 100% catch rate. Sneasel here would be an example. Normally he's pink but this is as shiny as Pokemon get.
(and possibly more difficulty to defeat - this is just speculation.) Every gameboard I've checked have come to consensus that they don't exist in Rumble World, and nobody's made a post claiming they have one.
Oh, and technically, you can get Pokemon with the perk "Superstar." They have a notably different appearance than others (spotlight/sparkles), but their coloring is the same. Example:
I'm not really sure what that Pokemon is, I'm gonna guess a Chinchou? I have no idea.
Hope this helps some. :)