TLDR - how to obtain the Tiny Flamefly:
step 1 - Head to Thorium Point in Searing Gorge and find the low level quest that sends you to Flamestar Post in Western Burning Steppes. OR you can try heading directly to Flamestar Post.
step 2 - Complete ALL quests from Flamestar Post. Once you've done this, you will be sent to Chiselgrip in Burning Steppes.
step 3 - Complete ALL quests from and associated with Chiselgrip. Once you've done this, you will be sent to either Flame Crest (horde) or Morgan's Vigil (alliance).
step 4 - Complete SEVEN! YUP! (alliance) or Not Fireflies, Flameflies (horde).
step 5 - Profit. :)
notes: Horde who are at war or hated with booty bay will need to raise their reputation with them before being able to complete the second to last quest for the flamefly.
Be careful not to destroy any of the quest items given to you while working on the quest chain as there is a chance you may need them further along the chain and will not be able to get them back later. Specifically the quest items received after starting on the Chiselgrip portion of the quest chain.
To begin the chain (if you are 80), you can pick up a breadcrumb quest from either a major city or from Thorium Point in Searing Gorge. This quest should send you first to Flamestar Post in Western Burning Steppes. Or you can try heading directly to Flamestar Post to see if there are quests that you can pick up without being sent there by another NPC.
Eventually you will be sent to the next quest hub in the zone, Chiselgrip. Once all quests have been completed your final destination will be Morgan's Vigil if you are alliance and I'm guessing Flame Crest for horde. An NPC will have a quest for you to capture 7 flameflies. The quest is called SEVEN! YUP! (alliance) and Not Fireflies, Flameflies (horde). Note: according to Kynole in the comments below, horde players will need to raise their reputation if you are hated with Booty Bay. One of the quest chain's NPC, Kibler, is part of the Booty Bay faction.
Upon completion you will be rewarded some gold, a choice between 4 uncommon items, and the flamefly companion. :) enjoy!
Thank you to the awesome users over at WarcraftPets.com for their reports on this pet!
Personal take on this new pet: It's cute and it will match well with the insect buff from an Underbelly Elixir. But! I would have preferred different coloring. Perhaps similar color scheme as Blacksting? In any case, I'm glad my firefly has a friend now! Too bad I still can't have more than one pet out at a time. Oh well, I guess I can just pretend that they're interacting with each other while hidden in my bags... talking about... insect-y... stuff? :P