I think my first shiny was indeed the red Gyarados, but since that doesn't count, the first one was a Butterfree in Gold. Ironically, it appeared when I headbutted a tree at the Lake of Rage.
I encountered two more shinies in the same game of Gold. And those were two Noctowl. In a row. Just like that.
Besides these, I have yet to encounter another shiny.