Jon wrote in post #16239512
Think about it. One purpose of any lens or filter coating is to reduce internal reflections that cause flare and glare. But each time light passes through a 10-stop filter it's attenuated by 10 full stops. That means that non-imaging light is reduced by, first, the 10 stops from the initial pass through the filter and second, by the 10 additional stops from each reflection inside the filter. The second purpose of coating is to increase transmission through the glass; the exact opposite purpose of a ND filter.
I thought the problem with filters and flare is that some of the light will reflect from the lens/camera components onto the rear part of the filter, then reflect from that side of the filter back onto the sensor. Like in the left-hand image here - LINK
So the light causing the flare has only passed through the filter once. Yes, it is diminished by 10-stops doing so, but so is your subject light - so the flare is the same brightness, proportionately, as if you'd used a clear filter.
But a multi-coated filter will reflect less light back into the camera than a single-coated filter. So it should produce less flare.