Typically, vents on water tanks are sized about the same size as inlets or outlets (IE, same nominal pipe size). Sizing them this way nearly always makes them substantially oversized for a given flowrate. But, water tank vents are fairly cheap, and owners don't want to see a 4" vent on a tank with 36" suctions, so that's the way it's done.
Occasionally, people come up with "what if the pipe breaks" or "what if the manhole cover pops off" type questions, and in those cases, you may need a larger vent.
One source for flow data is the ASHRAE Handbook of Fundamentals. It includes flow data for ducts that include an exhaust hood similar to a typical mushroom-style tank vent, as well as factors for screens, abrupt inlets, ells, etc. It's approximate, since you're not actually putting the fittings on a duct, but it'll be close enough for most purposes. Refer specifically to the older versions of the H.O.F. The newer ones either didn't have all the data (IE, showed exhaust but not intake factor for that hood) or perhaps put that data in other volumes. An HVAC engineer could probably point you to this info fairly easily. The flow factors give the relation between the pressure drop and the velocity, so that's how you get from one to the other.
A second source of information is published flow factors from vent manufacturers. Varec (currently made by Tyco) and Shand and Jurs both have "free vents" for which test data are available showing flow rates versus pressure (I think Varec's data is available online). I have seen Greenheck vents that show a flow rate on the drawing, but they don't show the basis for the flow rate. The Varec and Tyco Free Vents are only made in sizes up to 12" or so, but that size is liable to move more air than you need. You may also run across Groth vents; I haven't dealt with them in a while, though.
You can treat the vent as simply being a hole in the tank, and apply Bernouli's equation between the interior of the tank (pressure = 2", velocity = 0) and the vent neck (pressure = 0, velocity unknown) to get another idea of flow velocity. Of course, this doesn't allow for screen or geometry restrictions. But it'll give you a minimum area that is required.
It should be fairly simple to make up a flow-testing station for vents. However, it is even simpler to bump the vent size up a couple of sizes if anyone is concerned about it, and so I haven't seen any tests done.
FYI, I typically use 1" of water (IE, 5 PSF) for venting calculations. This is somewhat arbitrary, as the AWWA tank codes don't specify this pressure. But API-650 and API-620 both allow 1"/ 5 PSF for internal vacuum design. For venting from the tank, you could work through the API-620 design of the roof (assuming a steel tank) & anchorage to derive a higher allowable pressure (or up to the dead weight of the roof if it's concrete). Usually, large steel tanks are not good for much more pressure than the weight of the roof plate.
API tanks include allowances for sudden weather changes (cold rain on hot roof) and fire exposure (contents boiling off), but water tank flow rates are usually based on water movement only. Typically, calculations for venting do not include a safety factor, but sizing tends to be inherently conservative.
