There is no certain knowledge about it, according to the first series to last one (korra).
But this is seems how is it works;
Actually there is no reincarnation, there are just some sprits, and when a human's sprit bounded with a sprit from sprits world, actually the one from the sprit world caryying the knowledge and experiences and making a bridge/connection between these sprits and just passes to other nation.
You see when the bridge collapsed(unbounding raava from korra's sprit and destruction of her), all connection to past lives disappeared.
Based on uncle iroh, we may say when you die, your sprit is going back to sprit world or the other explanation when you were in sprit world if your body dies, you stuck in the sprit world. Like aiwei or commander zhao.
As conclusion, seems there is no sign of reincarnation. This is just assumed as reincarnation.