The flower is most probably Beach Morning Glory, Ipomoea pes-caprae. Pes-cabrae means literally "goat's foot" (shape of the leaves) so is also called Goat's foot creeper and bayhops.

A good early coloniser and stabilizer of sand dunes in that case. Is not transported by animals as is said in the article; the plant is salt tolerant with floating seeds, able to cross the ocean alone with the sea currents

Ipomoea are normally poisonous (not eaten by most animals) but this species has some medicinal uses. Used as poultice from Brazil to Australia to alleviate cuts, it seems.

There is a second species also. Monocot in this case. I'm not able to identify it with that photo but Spinifex would be my first try (even better to fight against erosion and keep the soil in place).

Fascinating history.