The DUP – which voted against only flying the Union flag on designated days in Belfast – has voted in favour of the policy in another council.
At the local authority's headquarters, only the council flag is flown.
Until 2000, the Union flag had flown on designated days.
After that, no national flag was flown for "cross-community purposes", an Alliance councillor said.
Sinn Fein members voted to maintain the no Union flag policy on Monday.
Alliance councillor Patrick Clarke said the DUP and Sinn Fein must clarify their position on the Union flag.
He said: "I welcome the fact the DUP has supported the Alliance Party's policy for designated days, but they must clarify what has changed. Why did they propose this motion at Down Council when they were so against it in Belfast?"
"Likewise, Sinn Fein must explain why it is supportive of the Union flag flying on designated days in Belfast, but when it comes to a council area where they hold the majority of power they are reluctant to fully support the policy.
"Both the DUP and Sinn Fein must make its views clear – do they support a policy of designated days across Northern Ireland? There can be no room for ambiguity."
Mr Walker said he brought the issue forward "not to be divisive or sectarian but because of a culmination of cultural issues over language and signage. The unionist community needs to have their voices heard. We haven't had a gain for our culture in too long".
Sinn Fein councillor Liam Johnston said for him there was no difference between how his party colleagues acted in Belfast or in Down.
"Flags show a sign of marking territory and on both sides of the community they can spur grievances and hurt.
"To have both flags equal would be preferable, but in this case it's both or none.
"We want to keep our no-flag policy at Down to show we are a neutral environment for everyone and anybody, all members and sections of the community."