Can you give a musical example of where we can hear a harmonic slide? Perhaps that can give insight as to the technique you're after.
Aside from that there's not much I can think of as far as technique that would pull off the effect of a harmonic sliding.
Natural harmonics are static in location (Frets 5, 7, 12 and 17 are the easiest to hit) and can only make a sound like a slide when the string is bent.
You can do this by:
Using a whammy bar once you hit a harmonic (as previously mentioned),
From bending the string between the neck and the machineheads once you hit the harmonic(if that makes any sense, I can't think of a better way to describe it),
or you can buy a slide for a dollar or so, which is essentially a metal cylinder you fit on your finger and you slide it over the frets (although that generates a different sound from standard harmonics).
Anyway hope this helps some.
-Cease