New Zealanders were asked to choose which of five designs they preferred.
A second referendum will be held in March next year to decide whether to adopt the new flag, or keep the existing one.
About 43% of eligible voters are thought to have taken part in the referendum, which has divided opinion in New Zealand over its cost and timing.
Voting officially closes at 19:00 local time on Friday (06:00 GMT), with the Electoral Commission announcing a preliminary winner shortly afterwards.
But local media say the result could change once overseas ballots are taken into account and the final announcement will be made next week.
The decision to choose a new flag has been backed by Prime Minister John Key, who has said the current one is too similar to Australia's and that it is time to remove the Union Jack from the flag.
He said the turnout, which was higher than had been expected, showed "people are engaging" with the debate, the New Zealand Herald reports.
Four designs were initially announced in September and a fifth, Red Peak, was added weeks later after a social media lobbying campaign.
The entire exercise is expected to cost around NZ$27m (£12m

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