If Avatar Kyoshi was the oldest Avatar, who would qualify as the youngest Avatar. Would it be Aang?
If you mean the youngest to master all four elements, this doesn't seem to be addressed explicitly so far. Most likely Aang, but still, there's no mention of that I think.
However, there are two bits of evidence suggesting that it was indeed Aang:
No one expects the avatar to master the four elements early.
At the beginning of The Legend of Korra, when Korra is done with her firebending demonstration, she urges the elders to let her move on to airbending. The elders respond that she is rushing things too much.
So the elders are not expecting Korra to master all four elements yet. This suggests that, historically, it is uncommon for an avatar to master them at an early age.
Roku mastered the elements until his adulthood.
We also know that Roku was already an adult when he was still training, according to the visions he shows Aang.
The above clues suggest that it is not normal for an avatar to master the elements early. Aang did so at the age of 12, with only one year of training.
The reason both Aang and Wan mastered the four elements in a short period of time was because they were under much pressure (Vaatu and Sozin's comet), so maybe another avatar also did this even earlier - however, we don't know of other "big events" that would require an avatar to master the elements so quickly.
Conclusion is - most likely Aang, but unconfirmed.