Of course if I buy Amazon Prime from the aussie website then all products purchased from the aussie site will have free shipping.
So what if I buy an aussie Prime subscription and log on to the american site - will I still have free shipping from my aussie membership?
No. Your Amazon Prime (+Video) subscription only works for Amazon.com.au. There may be Amazon USA products on there that you can get delivered here for free but not directly on Amazon.com.
Example: https://www.amazon.com.au/gp/goldbox - See the [Deal from US] options.
Also, not all products on Amazon.com.au will have free shipping. Only those sold and/or fulfilled by Amazon itself. Third party sellers are not included in free Prime delivery.