Flying Mounts were introduced when the Burning Crusade went live, and are quite different from the regular ground mounts, they have different rules, and of course a different cost.
Regular Flying Mounts
You may only use your flying mount in Outland, and you will need to pay 800 gold for Expert training once you reach level 70. Fortunately, there's lots of quests and errands to do as you hit 70 for you to be able to get the money up for your first Flying mount, since all Quests reward a decent amount of gold instead of experience as you hit the current level cap, allowing you to round off your 800 gold in no time if you didn't have it already.
All players have the ability to buy their faction's trademark flying mount upon reaching 70 regardless of their reputation. For the Alliance, you may buy a Gryphon, and for the Horde, you may buy a Windrider.
To buy a Gryphon, you must first purchase the 800 gold Expert riding skill from Ilsa Busterbrew in Wildhammer Stronghold, located in Shadowmoon Valley. Once you do so, you may buy a Gryphon for 100 gold from Brunn Flamebeard, within the same Wildhammer Stronghold. This Gryphon will move at 60% speed both in land and air.
Available Gryphon Colors for Expert Riding include Ebon (Black), Snowy (White) and Golden (Brown).
To buy a Windrider, you must head to Shadowmoon Village in Shadowmoon Valley. There, you must speak with Olrokk to obtain your Expert riding skill, costing 800 gold, and then talk to Dama Wildmane at the Wyvern Stables to get your very own Windrider!
Available Windrider Colors for Expert Riding include Tawny (Brown), Blue, and Green.
Alternative for Engineers
In Shadowmoon Valley, should you have 350 skill in Engineering, you may visit either Jonathan Garret if you're Horde, or Niobe Whizzlespark if you're Alliance, within your respective Shadowmoon Valley strongholds, and they will have 2 schematics for you - Flying Machine Control, and Turbo-Charged Flying Machine Control.
Flying Machine Control is for the regular 60% ground and air riding, and you will have your very own airplane! but first, you need to find the materials, which are:
2 Adamantite Frame
30 Fel Iron Bar
8 Handful of Fel Iron Bolts
8 Star Wood
5 Adamantite Bar
4 Elemental Seaforium Charge
Once you have crafted your own Flying Machine, you will only need level 70 to ride it (and of course, Expert riding skill)!
Epic Flying Mounts
As you progress in your adventures at level 70, you may wish to advance your riding skill to Artisan, allowing you to ride mounts rivaling the speed of the normal flightpath speeds. This is a costly endeavor, one that many players spend hours upon hours saving up for, as it costs a whopping 5000 gold to train Artisan riding. The mounts, however, all average 200 gold, so all in all, you will need to procure 5200 gold in order to fly faster in Outland. The Artisan flying speed is 280% on air, 100% on ground, without factoring in any trinkets nor equipment.
As with regular flying mounts, you will need to buy your riding skill from Shadowmoon Valley's trainers, the same ones you visited for Expert riding skill. There is no discount at all with either stronghold as they're considered a separate entity from Horde and Alliance forces.
If you're Alliance, you have the option of picking between Red, Blue, Purple and Green Swift Gryphons.
If you're Horde, you have the option of picking between Yellow, Red, Purple and Green Swift Windriders.
Alternate Epic Flying Mounts
Turbo-Charged Flying Machine
Engineers have the option, once more, to craft their Turbo-Charged Flying Machine to replace the Swift Windrider or Gryphon. The components for the epic flying machine are as follows:
8 Khorium Power Cores
8 Felsteel Stabilizers
1 Hula Girl Doll
For the above, you will need:
2 Primal Earths
8 Primal Fires
24 Khorium Bars
32 Eternium Bars
13 Adamantite Bars
102 Fel Iron Bars
8 Star Wood
1 Mote of Fire
2 Mote of Earth
Between 80 and 100 gold for the Hula Girl Doll
Once you have crafted your Turbo-Charged Flying Machine, you're free to roam the skies ontop of your unique new mount!
Players who have been working with their reputation with Ogri'la and the Sha'tari Skyguard will also be able to buy Nether Rays from the Sha'tari Skyguard Outpost in Blackwind Landing, from the NPC named Grella. You will need Exalted with the Sha'tari Skyguard to be able to buy a Nether Ray, and naturally, epic riding skill.
To view our guide on how to obtain reputation with the Sha'tari Skyguard, click here.
Available Nether Ray Colors include Blue, Green, Purple, Red and Silver Nether Rays. You will receive a discount for being Exalted, so the total for any of them will be 160 gold as opposed to 200.
Players who have bought their Artisan riding skill are also able to undertake Netherwing's questlines, which include a plethora of daily quests in order for you to reach Exalted.
To view our guide on how to obtain reputation with Netherwing, click here.
Worth mentioning is that your first Netherdrake will be free, and subsequent purchases can be made from the Mount Vendor Drake Dealer Hurlunk in the Netherwing Ledge Outpost.
Available Netherdrake colors include Azure, Cobalt, Onyx, Purple, Veridian and Violet.
A special mount is available from the Cenarion Expedition; it requires Exalted with the Faction and a whopping 2000 gold in order to be able to buy one of these Hippogryphs, as opposed to the traditional 200 gold for most of the mounts. Worth noting is that you will actually pay 1600 gold thanks to the discount if you have Exalted.
To view our guide on how to reach Exalted with the Cenarion Expedition, click here.
Those wanting armored netherdrakes that have 310% flight speed will need to contend within the Arena and finish within the 0.5% best teams in their battlegroup, netting them the title of Gladiator for the next season, and this mount as a reward.
Ashes of Al'ar
Prince Kael'thas Sunstrider within the Tempest Keep's 25-man Instance "The Eye" has a very low drop chance for this unique epic flying mount, allowing you to fly at 310% should you obtain it.