Shinies in SPEE will be a lot more common than official games, probably a 1 in 512 chance.
The roll for shinies are done directly after a battle, if you do get the roll, you'll isntantly be thrust into a shiny battle.
These shinies are inderpendednt of the area you're in, so you might even fight a shiny wurmple in the middle of the ocean.
Shinies will appear in v0.6. BUT make sure you scan them for an upcomming feature in v0.7
For every shiny you scan, you can turn one of your own fully evolved pokemon into a shiny. To make up for the fact you can't catch shinies themselves.
Although the turn-into-shiny feature won't be in v0.6, any you scan will still be counted in v0.7