Are you sure KM Engine is running? (Icon in menu bar?)
I'm not aware than KM needs anything in System Preferences > Accessibility.
However KM Engine should better be checkmarked in System Preferences > Security and Privacy > Privacy > Accessibility. But if KM Engine needs those permissions it will usually prompt you.
It looks like KM was having a problem with only the F1 key, for some reason. I reassigned the macro to the F18 and it works. I still don’t know why F1 is flaky.