Heavy, water-proof grease is a good idea.
Slipperiness isn't the reason for the grease. The goal here is to keep out moisture and oxygen, thereby discouraging oxidation. Aluminum oxide is especially problematic, as its molecules are substantially larger than the aluminum molecules in your seat post. Oxidation will cause it to jam very tightly.
In general, you don't have to worry your seat post slipping. The surface of the seat post and seat tube are not perfectly smooth. The "high spots" will push the grease out of the way, in to the "low spots" where you might otherwise see moisture and oxygen.
It doesn't take much grease to do the trick, since the seat post is already quite snug. Just make sure it's all covered.
In some cases it's possible for grease to get trapped and not be able to squeeze out, giving a result similar to hydroplaning. You tighten & tighten and things are still slippery. It's not likely in this case, because the seat post clamp is narrow.
For overkill, you can even use anti-seize: