How does one measure the efficiency of an exhaust vent?

Efficiency is not the metric, so they have no idea what you are talking about. How about room air exchanges per hour? That would be the volume of air removed per hour divided by volume (length x width x height) of air in the room. But then you would have to find guidelines relative to usage of the room.

You would also have to figure out how much air was coming into the room to replace the air being sucked out by the exhaust fan. For the exhaust fan to be 100% effective, IMO, it would need an unlimited amount of replacement air, like a open window that had no restrictions, which would be something that you, yourself, could control.

Is there enough info on the fan to find it’s cubic feet per minute (CPM) rate?

From there:
Air changes per minute = room volume in cubic feet / fan CPM

Air changes per hour = 60 x Air changes per minute

I found a brief explanation here: Air Changes per Hour (ACH & ACPH) Calculator Tool

The actual Cubic Feet per Minute.

I worked in a manufacturing facility that the EH&S person came out to check the exhaust fan in a closed enclosure with a unit that measured CFM (put it in the gap with door up 3 inches and filled the gap with Styrofoam. It was supposed to 200 CFM and was only 75. We had to add another exhaust fan on the roof (30 feet away with three 90 degree bends, guess why it was so low).

Thanks. That all helps. I am just super frustrated that the company we pay to oversee health and safety has no resources for this. And there should be fresh air return vents, but they would have to be punched through the ceiling because no exterior walls, and the doors must be closed for the rooms to function.

I am a novice at this, but I seem to remember watching a kiln be put in a closet in an existing classroom. For a gas kiln you have to have a vent that allows air in and out.

This link should give you all the details required for your kiln. Scroll down to where you see, “Kiiln Room Conditions & Venting”. There you will find several links that should be helpful to you.
https://hotkilns.com/support/pottery-kiln-knowledgebase/installation-checklist

This link explains the details of venting a dark room. Placement of vents is important, and it’s especially important that you filter the air coming in so that it doesn’t bring in dust. Scroll down to the paragraph concerning ventilation. https://www.photographytips.com/page.cfm/4710

I’m sure other people here can help you find the airflow of existing vents.

Vents are usually measured in CFM, Cubic Feet Per minute.
Here are some typical numbers:
A bathroom exhaust fan is 85 CFM.
A window fan can be something like 200 CFM

Without data all you have is an opinion so… Buy one of these: Wind Speed Meter, Anemometer.

A unit in the $20–30 range will give you good numbers. Hold the meter in front of the vent and measure the speed across the opening. . Measure in multiple places to get an average flow across the surface area. Use that number and the area of the across the opening to get volume flow. Then calculate room volume. With that info you can calculate the exchange rate.

Buy the unit first! You need to have your own data to prove or disprove their claims.
Make it part of a class project. Have 2 teams independently measure it and compare answers.
Data carries the weight you need.

So what I would probably be looking for is airchanges per hour. This takes into account the size of the space being ventilated and how much ventilation is required. Using hospitals as an example a standard hospital room requires something like 6 air changes an hour. You can manage this almost by accident, doors open king and closing people moving etc. An operating theatre will require more like 20+ air changes an hour ie the whole room volume changed every 3 minutes which is much harder to achieve and even for a single operating theatre will involve a pretty significant air handling plant. We get the ventilation checked every year – someone comes along and measures how much air is moved by the vents and exhausts and compares to the size of the room to make sure it is acceptable.

(A 747 can manage 60 air changes per hour, 30 from recirculated air via a hepa and an additional 30 of fresh air from out side. It’s what causes that annoying noise on board.)

For your examples where there are potentially noxious chemicals being used you would need at least 12 to 15 air changes I would have thought.