If Scotland became independent, what would happen to Australia and New Zealand’s flags (since their designs have the Union Jack, which uses a blue background and white saltire to represent Scotland)?
Nothing. Australia and New Zealand are fully independent countries and they can have any flag they want. They would have the option of altering their flag, but they wouldn’t have to if they didn’t want to (and if they were going to go through the trouble of changing their flags it would probably be to something entirely different.)
I also don’t imagine the United Kingdom would change its flag even if Scotland gained independence. The Union Flag is a classic design with a lot of history behind it, and from what I understand it’s pretty well-loved in Britain.