Interesting WI, Darkest.
What you have to realise here is what Thomas Kuhn calls "incommensurability". Strictly speaking, Lavoisier didn't discover oxygen either, because what he called oxygen is different from what we call oxygen. He thought it was a key component of all acids, which is incorrect, and didn't necessarily think of it as a chemical element (or to be more accurate, he thought of other things like heat, 'caloric' in the same terms as he thought about chemical elements).
Having said that, I could see Hooke making the same kind of discoveries as Priestley did 100 years later, which arguably had more to do with the discovery of oxygen IMO than what Lavoisier did. I wonder if we could avoid the phlogiston business this time. Personally, I doubt it, because phlogiston seems more logical (something comes OUT of burning things - you instinctively think it's right because you're used to flames and smoke coming out of burning things and leaving a smaller pile of ash than the thing you started with) than oxygen (something goes IN to burning things - which you can only confirm when you have a really accurate balance to show that it's gained weight).
The 1670s was a period of intense interest in gases and vacuums, so I could see Hooke identifying it as a gas to begin with, which would save a lot of headaches. But without the accurate balances of 100 years later, I suspect phlogiston-type theories would be the mainstay for a while.
