Well it does say it is in a lost age of time, so this show is probably based on China not only in the past, but in an alternative universe, which means a different world that is similar to Earth. Humans have been around for only 500,000 years, so if it was in this world it would have to have been any time around then, either BC or AD. Soemthin' teels me though that the period was just around the time of Ancient China which i think is somehwere around the 2000 BC-100 BC era. Either that or it really is the 1800's. What with those mehcanical operatable machines and all that. The Fire Nation used them anyway.
If all four natiosn are at a different time zone, here's how I would put it:
FN: 1850-1912
WT: 1400-1600
EK: 1400-1600
AN: 2000 BC-100 AD