do I need to multiply the outdoor air flow rate according to zone multiplier?

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Do the experiment yourself:

• Take an E+ example file that leverages DesignSpecification:OutdoorAir, eg: 5ZoneAirCooled.idf
• Add the output variable Output:Variable,*,Air System Outdoor Air Mass Flow Rate,Monthly;
• Create another version were you assign to each Zone a multiplier of 3
• Loop at the output, and decide...

Zone mult of 1: Air System Outdoor Air Mass Flow Rate sums to annually 1.61, one mult of 3 is 4.83. That does look like it's getting multiplied by 3.

Caveat: If you have hardsized your loop or outdoor air flow rates to a wrong value, it can get capped... so watch out for this.

Please do not read generalize this answer blindly. DesignSpecification:OutdoorAir objects for example are indeed affected by zone multipliers, but there are a number of airflow related objects that aren't (Fan:ZoneExhaust` for example). Please read this question for more info.