Westerners would say that August is the middle of winter in Australia. But the Anangu recognize five seasons, not four. August begins the season of "Piriyakutu", sort of a false "spring". It's followed around December by a hot dry season called "Mai Wiyaringkupai". January/February/March (aka "Itjanu") is the wettest season, but Piriyakutu can bring some rain, too. Food plants flower in both seasons (more prolifically in Itjanu, but I assume less comfortable for tourists to enjoy since it'll be 100 degrees out here).
Uluru receives about 12" of rain annually. That's roughly the same precipitation as Boise, Idaho. So, more than lack of rain, the real problem is infertile soil. Few Australian trees are deciduous, which means no leaf litter to produce nutrient-rich humus. There are no volcanoes nearby. No glaciers ever brought top soil here. There are no mountains to provide a valley which could collect eroded minerals. And it's been hundreds of millions of years since oceans deposited dead sea life here. So, that annual rain adds up to just one thing: leached soil.
Despite those challenges, life finds a way. I saw lots of flowers on my walk.

Lots of yellow flowers on this bush, approximately 4 feet tall.

Tiny pink and white flowers on this bush.

This was a flower about 18" tall with striking, bright yellow flowers.

This ground cover had tiny aster-like purple flowers with yellow centers.

This was another ground cover with pretty purple flowers.