It does need some air supposedly. Oxygenating it specifically I don't think would be beneficial. Basic instructions are to not allow the water to boil too much, or even cut off the heat before it gets to boiling (boiling is too hot for the tea anyway). Then sometimes I pour the tea back and forth between two jars a couple times to get some more air dissolved.
Homebrew equipment that could be used in making KT, well swing top bottles are really nice for bottling KT if you want it to be carbonated. Depending on how much you're going to make you could heat the water in one of your kettles for the tea.