Don't kill me, but the one time I got lucky enough to get a shiny starter pokemon,(tepig) I ended up deleting save data without trading it to another game.
The others I've gotten, I believe I caught a diglett with a blue nose once, and there was a green onix one time. Restarted game without trading as well for those guys.
The last shiny pokemon I encountered that I still have, would be my shiny Golduck, that I caught as a Psyduck while ev training the shiny Gible that you get in Pokemon Black 2 lol
I named him Preyas :D