You’re about as likely to win lotto as change an election outcome where any large number of voters are participating, so thinking hard about strategy on the coming flag referendum makes about as much sense as thinking hard about the numbers you’d pick for lotto.
Depending on what the polling looks like closer to the referendum, there could be strategic considerations that come into play – if you enjoy that sort of thing. But it’s a bit complicated. I used to teach this stuff at Canterbury so re-worked one of my old STV examples to put it into a flag context. It isn’t hard to construct examples in which a small number of voters lying about their first and second choices (claiming that their second choice is in fact their most preferred choice) are able to see their second choice win rather than their least-favoured option. Whether that is possible in the real world depends on what others’ preferences really are, and how much you know about them.
More worryingly, to my mind, is that STV does not necessarily choose a Condorcet Winner. What is a Condorcet Winner? Imagine that the Koru design would beat any of the other four flags in a head-to-head vote. That flag would be the Condorcet Winner. But it will not necessarily be the flag chosen under a preferential ballot, depending on how things work out. Since voters will be ranking all the flags on their ballots anyway, it would be simple for them to check first whether any flag would actually beat each and every one of the others in a head-to-head contest. Maybe the preference ballot would also select the Condorcet Winner, if there is one. But it might not. If the Koru design were the second choice of most voters but the first choice of few, it would be eliminated in the first round of the preference balloting – even though the flag that’s the second choice of most voters would likely win against any other flag in a head-to-head race.
So if we’re having urgent changes anyway, one worth making would be having the Electoral Commission check for a Condorcet Winner before running the elimination rounds. Or, perhaps even more fun: they could release the data after the vote but not check for a Condorcet Winner. Then we could all spend years arguing about how the country chose the wrong flag.