Chris

The Union Jack was created on the instructions of James I/VI to fly on his naval vessels, leading to the creation of a common naval force for England and Scotland a century before the formal union of the parliaments.

As the union of the crowns was the reason for the flag, and the crowns would remain united under the version of independence being touted by the separatists, the union flag would have a continuing role and anyone who wished to show loyalty to the Crown could justifiably continue to fly the flag.

If you think that answer fails to give you any concrete idea of how things would actually play out in practical reality, consider yourself lucky that you don't live here in Scotland, where we are daily asked to swallow gravity-defying nationalist assertions with barely a thread of evidence or reason.