In order to start the quest required to purchase the Flying Carpet travel to the Savage Wilds Server.
Once there, either /warp Voter or travel to E7 in the town of Muruun.
When you arrive, head over to the building pictured.
Inside, talk to Ali Zendag Flying Carpet Master, he's levitating Inside.
Speak to Ali Zendag, He will instruct you to find his sister, Alita Zendag in C9 of Savage Wilds.
Travel to C9 and enter the Cistern.
When you enter, go through the door and turn left. Then go down a very long ramp. This will open up into a large room. After jumping down into the lower portion of the room, where you will find several 3 Skull Giant aligators you will find Alita Zendag in C8.
Speak with her and she will give you what Ali is looking for.
Once you return to Ali, you can purchase a Fancy Flying Carpet or a Flying carpet. The difference is only cosmetic.
If you want to trade it in for a cloud, I recommend that you get the regular carpet.
To trade in for a Cloud, outside of the building and to the left to see Nimbus, Cloud Walker.
On the next menu, select the item that you wish to trade for the cloud, so if you have a Regular Flying carpet, select Magic Carpet(Flying). She will give you a yellow cloud.
If you want a blue cloud, talk to her again and select the bottom option.
Once you have either the carpet or the cloud, place it onto your hotbar. When it is active, you will fly.
Once you have it, head over to this page to set your flight speed increase and flight speed decrease hotkeys!