The Labour Party put in a minority report saying it was "strongly opposed" to the bill because of the order of the wording.
Labour MPs argued that a clear vote on change in the first referendum could save up to $6.8 million in the costs of a second referendum.
The majority report rejected that, saying the Electoral Commission advice was that it would only save $2.27 million net, given costs already incurred.
The committee also rejected suggestions to change the timing of the referendums so that the first did not coincide with Anzac commemorations for the centenary of the Gallipoli campaign.
The National MPs on the committee said the current debate did not detract from the service of veterans, and the timing would allow it to be held well in advance of the 2017 election campaign "to ensure the flag debate is not eclipsed by election campaign issues.
"The only significant amendment is to include a 'regulated period' for advertising for the referendum to ensure that MPs do not use taxpayer funds or resources to campaign on the flag.
There are no limits on advertising spending.
The $26 million flag process has been criticised as a waste of money after low attendance at public meetings.
The Flag Consideration Panel has defended that, saying there has been intense debate on social media about the issue and almost 5000 possible designs submitted.
The deadline for flag designs from the public is 16 July and the panel will select a shortlist of four after that.
The first referendum will be in November and December, and voters can rank their preferred choices of the alternatives.
NZ First leader Winston Peters said opponents to changing the flag should ruin their first referendum ballot paper by writing "Keep Our Flag" across it instead of ranking the alternatives.
"The first question should be: 'do we want a change?' Otherwise there's no point in consulting the public about new designs.
"He said the low attendance at public meetings showed New Zealanders had turned their back on the whole process.