I've thought about this a bit, and I think I might have an idea of what's causing this behavior.
This seems to be limited (or at least, happen the most frequently) with Luxeon Vs. I think their serial/parallel arrangement may allow this phenomenon to happen.
I think what is happening is that a high resistance "short" is allowed to form between the anode of the downstream diodes (which is also the cathode of the upstream diodes) to the heat sink slug. Then, the "-" terminal ESD diode allows this current to flow to the negative terminal by forward-biasing the ESD diode.
Here's a diagram:
At low current, the combination of the forward voltage of the "-" terminal ESD diode, plus the voltage across R(leak) when very low current flows is actually lower than the Vf of the downstream LED diodes, causing the current to flow through that path, rather than through the LED part. But, when enough current flows, Vz2+V(leak) equal the Vf of the second set of diodes, so current starts to flow through them. R(leak) might be variable/intermittent, so higher currents (1-10mA and higher), R(leak) could increase substantially; and at some critical point become intermittent, causing the flickering we observe.
I tested my WW0T Lux V and measured the voltage between the slug and "-" terminal (measuring Vz2). At ~1mA, Vz2 was about 0.6V. However, once I hit about 2.5mA, Vz2 started to drop, and continued to drop until I hit about 20mA, at which point all 4 dies were evenly lit. So the current through the "-" ESD diode was dropping, probably because R(leak) was increasing, no longer bypassing significant current from the downstream LED diodes.
This may be a byproduct of the way the luxeon V is constructed. On the silicon submount of all other luxeons, there are 2 contact pads. These contact solder balls on the bottom of the led die. Each contact pad has a zener diode to the slug (the ESD diodes), and a bond wire to the power leads.
However, on the luxeon V, there are 3 contact pads on the silicon submount. The "outer" ones serve the same purpose as the 2 pads on regular luxeons, and have the same connections. However, the central pad serves as a bridge to join the two series connected dies. That pad is supposed to be completely floating and isolated from everything, but I suspect that high resistance connections to the slug can form, causing the behavior we see above.
This is probably another reason why the Luxeon V will probably eventually be dumped, as it seems there are quite a few challenges to the packaging that you don't see in a single die LED.