Yes, shiny pokémon can be found fishing, too.
The only surfire way is to keep restarting until you get one. But shinies are very hard to get.
Personally i don't know, although my friend told me that he kept running into the same Pokemon while in a cave and then eventually found one.
You have to get lucky
fish on route 223
you can't catch it in the wild you have to transfer it from Pokemon ranger or if your lucky enough (like shinies) you might find a green man inside the pokemart of sunyshore or buy a action replay regular edition
You can find them if you fish in route 224.
You can fish with a super rod
The most expensive fish is Platinum Arrowana. Its cost is around $80,000.
shiney Pokemon are pretty much versions of the normal ones that are a different color. but some shinies may learn different moves non-shinies can't.
fish with good rod in Eterna City
You either find them randomly, or you use a chain with the pokeradar :)
Fish at Canalave City with Super Rod.