Ouch - there's some bad advice being given here.
It's vital to keep the LED junction temperature below its maximum limit of 145 degrees C. If you have poor thermal conductivity from the LED to the air, your hand, or some other sink of constant temperature, the LED will overheat and die. There are several thermal resistances in the path from the LED to the ultimate sink. All are in series, and the temperature differentials add.
A convenient and common unit of measurement of thermal resistance is degrees C per watt. If you have, for example, a total thermal resistance from the LED junction to the air of 30 degrees C per watt and the LED is dissipating 3 watts of heat, then its temperature relative to the air will be 30 * 3 = 90 degrees. If the air is 25 C, then, the LED temperature will be 115 degrees C, well within its spec. Note that the internal thermal resistance from the LED junction to its mounting pad is 6.9 degrees C per watt. So you need to keep the pad temperature below 124 C if you're running the LED at 3 watts. Assuming an ambient temperature of 25 C, that means you can tolerate a temperature differential from the pad to the air of 99 C. This in turn means that you can tolerate no more than a total of 33 degrees C per watt thermal resistance from the mounting pad to ambient if you're running the LED at 3 watts. (Strictly speaking, the 3 watts is the heat dissipation, which would require putting a bit more into the LED to account for the light output.)
The thermal resistance of a piece of material like a spacer is directly proportional to the thickness, inversely proportional to the area, and inversely proportional to the thermal conductivity of the material.
So let's look at the thermal resistance of spacers made from several materials that have been mentioned here and a few others. I've calculated the resistance for a spacer thickness of 0.030" and the area of a Seoul P4 LED mounting pad (0.2" diameter). Instead of the resistance in degrees C per watt, the table shows the temperature differential across the spacer for an LED dissipation of 3 watts. This is how much hotter the top of the spacer will be than the bottom with 3 watts of heat passing through it. The resistance in degrees C per watt is 1/3 this value. Remember, you have a total of 99 degrees for the entire path from the LED pad to the outside world. You don't want to use up any more of the allotment in the spacer than you have to.
MATERIAL ---- TEMP RISE FOR 3 WATTS (deg. C)
Copper (pure) -------------- 0.3
Aluminum (pure) ------------ 0.5
Alumina (ceramic) ----------- 6.3
Arctic Silver Epoxy ---------- 5.0
Arctic Silver Compound ----- 12.7
Arctic Alumina Compound --- 28.2
Kapton (HN type) --------- 940
It should be obvious from the list why layered Kapton tape isn't a good choice for a spacer. (And the table value doesn't include interspersed layers of adhesive of unknown thermal conductivity.) Using paint or fingernail polish is a crap shoot -- you'll have no idea of its thickness or thermal conductivity. But remember, the thinner the layer is, the less important its thermal conductivity. If you use copper or aluminum for the spacer itself, you can get by with a thin layer of poorer material on one or both sides. But even 0.001 inch of Kapton tape, with the adhesive removed, will get you a 31 degree rise at 3 watts. That's a full 1/3 of your total thermal budget.
The manufacturer of the Arctic Alumina and Arctic Silver materials gives no thermal conductivity specification for Arctic Alumina epoxy, which is why you don't see it on this list. The lack of any specification is in itself enough to steer me away from it.
I usually use around 0.005" (a wild guess) of Arctic Silver epoxy (about 2.5 degree rise at 3 watts) for electrical insulation, a copper spacer (0.3 degree), and perhaps 0.002" of Arctic Silver compound (about 1 degree) under the LED, for a total of around 4 degrees. This way I can get by with a poorer path from there to the outside than if I had blown more of the thermal budget at the spacer.
Stars have an electrically isolated mounting pad (at least every one I've encountered does), so you only need a very, very thin layer of compound or epoxy on each surface of the spacer, with no worry about electrical insulation.
Of course, you can ignore all this and take the experimental approach. Just try whatever's handy. The Seoul LED will tell you when it gets too hot -- you'll learn to recognize that blue color right away once you've seen it.
c_c