You live in Australia, correct? I have no idea what the current covid and/or vaccination situation is there so I can’t do more than speculate.
What I have heard on the BBC podcasts I follow is that covid is relatively contained in Australia at the moment. So I would suggest first getting the flu vaccination and also scheduling your covid vaccination for 2 weeks after you can get your flu shot. My thinking is the flu vaccine is a relatively straight forward single dose, but the covid vaccine process can take longer to work through.
Out of curiosity which covid vaccine would you be getting? I suppose if you are getting a two dose version of the covid vaccine you could also get the first covid, wait 2 weeks then get the flu jab, then wait two weeks more and get your covid booster jab.
Bottom line: If your situation is anything like what we’ve faced in the US, it will probably boil down to what is available and when it is available.