Interesting. I’d never heard of this before.
Some quick Googling indicates that cyano glycoside is released on crushing the seeds. This in turn can result in the release of hydrogen cyanide. The hydrogen cyanide would be trivial to wash out as it would be soluble in water, but it seems unclear if cyano glycoside is a problem. There would presumably be some hydrogen cyanide released in your body during the digestion process as not all of it would have been released during the crushing process. I can’t find any information regarding how much is left, or how much can be released during digestion - possibly because no one knows.
I’ve never heard of people getting ill from flax seeds though. I used to consume quite large quantities of them myself at one point.