I've seen referencs to "such and such an aircraft has a flying tail". I
imagine it means "out of the slipstream", but it sound sort of dumb to
me. Is it more than marketspeak? Does "flying tail" actually mean
something?

Wasn't it "all-flying tail"? And didn't it refer to stabilators? I
took it to mean that instead of changing the chord, as with elevators,
the angle of attack of the horizontal stabilizer changed. The
implication might have been that there was less drag, or less change
of drag, that way.

I've always heard it to mean stabilator, for pitch control, so that the the
entire horizontal tail surface is "flown." This would be as
opposed/compared to a fixed stabilizer and moveable elevator, which has the
effect of variable camber.

The same can be done with the vertical tail, although the only place I have
personally seen it was a Folker Triplane replica. It flew quite well, at
the hands of a very good pilot, but what I saw indicated that I was NOT
qualified to try it. (Back then, planes flew much closer to people on the
ground, and observers could be quite close to the runway, so the required
rudder work was more visible.)

Peter