They aren't in the game. I expect them to be added later, I think after the servers are fixed and all we will slowly start seeing a lot more added to the game such as friendly battles, trading, and yes, shinnies. Could take a while though.
Yeah I agree, I think there's a lot of stuff to be fixed before Niantic add more features but I can't wait to see what's in store for Go!
I don't actually know if they'll be added in the future as Pokemon GO seems to be a Gen 1 specific game and shinies weren't introduced until Gen 2 (I think). Then again, eggs weren't in Gen 1 either so... who knows.
They confirmed that at some point all Pokemon will be available in Pokemon Go, so hopefully that means shinies too!