When did it actually happen? When I started D&D, kobolds were like, goblins, if goblins were too hardcore/dangerous for you.
The first time I really came across the idea that they were really associated with dragons was Dragon Mountain, in 1993, but it seemed like it wasn't an entirely new concept then. And the Monstrous Manual from the same year (both this and Dragon Mountain illustrated in part by the incredible DiTerlizzi, offering us both flat-faced and ratlike visions of kobolds) doesn't mention dragons.
Yet by 3E, kobolds are solidly little dragon-people.