Certified GKH Gardening Expert
This appears to be a serious wound or sunburn of the bark and underlying growing layer of the trunk. Opportunistic wood decay fungus infection has occurred and there is no quick fix. Horticultural oil is not appropriate treatment.
The additional complication is that the wounding appears to be so severe that it has affected the conductive tissue (uptake of water and nutrients) on that side of the tree and caused one-sided die-back in the foliar crown.
The best you can do and hope for is to suppress the advance of the wood rot fungal disease by providing best conditions for tree health and wound closure. Good soil fertility and water management are essential.
If mine, I would also apply a systemic fungicide with hope of suppressing the advance of the disease. Agrifos Systemic Fungicide or other brand of phosphite formulation acts to build tree resistance to disease. It is not a direct cure.
Apply to the tree trunk along with a bark penetrating surfactant like PentraBark. I don't know where you can get these in Australia, but check Amazon or contact the manufacturer for retail distrubutor info.
Do not remove lower foliage, top or thin tree excessively; encourage foliar shading of the tree trunk and scaffold limbs.
From the photos and from my considerable experience with this species, it appears to be a severe condition and the tree may not fully recover.
By the way it's one of my favorite trees. Delonix regia. Here in Thailand it is called "tail of the peacock", in Hawaii and Florida USA "royal poinciana" and "flamboyant tree".
Wish I had better news and solution for you. Good luck, Don