The last common ancestor between birds and snakes would have been alive some 250+ million years ago. Not long after that, the ancestors of birds and crocodiles split ways too. So the "missing link" between birds and non-avian reptiles was long dead before primates, let alone humans, were a thing.

What's really going on is that Quetzalcoatl, Kulkulkan, and related figures in Mesoamerica are pulling from some common themes in North America, which also give us Awanyu in the Southwest, the winged Unktehila of the Plains, and the Horned Serpents of the Eastern Woodlands. The specifics of these beings all very but what they have in common is that they're "liminal creatures."

The Snake is common seen as the emblematic animal of the underworld; birds, conversely, are the emblematic animal of the upperworld. Deer and, to a lesser extent, cats like the puma or jaguar are the emblematic creatures of the middle, mortal world.

So a snake with feathers, or antlers in the case of the Horned Serpent, or both in the case of the winged version of the Unktehila, are being that mix aspects of the various realms of existence. They stand on the threshold, neither here nor there, not quite one thing or another. That's what liminality means. They defy categorization, which makes them transgressive; they're outcasts that don't belong anywhere. It also makes them powerful, since they can pull from both sides as needed.