To obtain Reins of the Green Proto-Drake, you must first become Revered with The Oracles, a faction located in Sholazar Basin.
Once you become Revered, you can purchase a Mysterious Egg, which after three days becomes a Cracked Egg. This egg, when looted, has a chance to drop one of 4 mini-pets, this mount, or some aged yolk.
Reins of the Green Proto-Drake has a 5% drop rate.

You can only buy one egg at a time (due to its "Unique" tag), and it takes three days to hatch. That means you only have two chance per week to obtain this mount. Hope this was clear and helpful.