It seems incessantly hot there all the time. If you want to see wildlife, you need to go in the beginning of the Wet. In the middle of the Dry, in June or July, it may be the most comfortable to travel, but you won't see much in the way of critters. They were out a bit at night in Kakadu, but not so you'd notice much. Different seasons will have different mosquito levels however.
Flies are another matter.
They were at their worst in the Center at Ayer's Rock, and I never adjusted to them. The flies don't bite fortunately, so it's not like dealing with the horseflies in the Arctic. But they hover around you in clouds and constantly patter against your face. It's extremely distracting. I'm usually not bothered by bugs, but I couldn't abide these.