Mr Flaunty is paid $78,900 and Mr Gillon $79,000 for their two roles respectively.
The Local Government (Auckland Council) Amendment Bill (No 3), Mr Ngaro said, would prevent double-dipping and protect against conflicts of interest.
He said the law closes a loophole that allowed local board members in Auckland to serve on multiple local boards at the same time.
The new law will not stop candidates from standing for more than one local board, but they will only be entitled to hold one elected board position.
Candidates standing for more than one board will have to publicly state the boards they are standing in and the order of priority that would apply in the event they are successfully elected to more than one board.
Mr Ngaro said Parliament agreed that the law as it stood meant too much power could be concentrated in the hands of too few people.
The law comes into effect for October's local body elections.
When the Government set up the Super City in 2010, it prohibited people serving as a councillor and Local Board member.
Mr Gillon said the bill was a political stunt which used the conflict of interest argument as a trojan horse to get it through.
It was ridiculous, he said, to think there could be a conflict of interest for one person to serve on two or more boards.
There had never been an occasion of one board decision affecting another board.
Mr Gillon said he made it clear in the electoral booklet sent to voters he was standing for two boards, and got elected by the will of the people.
He said that when he was a North Shore city councillor he served the equivalent of three local boards and got a deep understanding of communities of the Shore.
Ms Whyte and Mr Flaunty could not be immediately reached for comment.
Mr Flaunty's telephone voice message said: "I'm more often than not in meetings."
