I had been wondering this myself since I help out at a friends flower farm and we also grow this type of Eucalyptus so I looked into it.
It would seem that you can use it in very similar ways to Eucalyptus globulus or E. radiata (the essential oils of both of these are discussed in the Aromatic Medicine course if you are taking the CHP program). Instead of making an essential oil however you can make an infused oil with any part of the plant including the root. You could leave it as an oil or make into a salve. Either of these would be a good base for a home made ‘chest rub’ for coughs and colds or as a bug repellent.
The scent can also help clear the sinuses and uplift ones mood.
It seems that this species of Eucalyptus has some similar constituents in the essential oil as the other species of Eucalyptus and therefore is likely to have anti-bacterial and fungal action. Infused oil could be used on the skin once again to help healing of a wound, a chesty cough, etc. But it is best to keep it as an oil infusion or salve rather than the essential oil, since the oils in the plant can be very caustic and toxic.
I have come across a couple of mentions about it being drunk as a tea, with just 2 leaves per cup, or made into lozenges, for example, but I do not know enough about the specific cautions or contraindications for internal use, so I would highly recommend looking into this further. A tincture would also be an interesting thing to research further since I have found tinctures for sale on the internet, but am having a hard time finding reliable information on how to use it, it’s safety and dose.