As well as purchasing your mount, make sure you also purchase the riding skill that allows you to fly. There is one for Outland and, if you also want to fly in Azeroth, there is also a skill to purchase in Stormwind or Orgrimmar (depending on whether you're Alliance or Horde).
You need the Cataclysm expansion to be able to fly in Classic WoW zones (anything in Kalimdor or Eastern Kingdoms). Also, there are some ares flagged as no-flying, but as of 4.2 you can still summon a flying mount there. It won't take off, it will behave just like a ground mount.