Does the slippery feeling of bases always appear at certain pH?
There probably is no one pH level where things get slippery. Capacity to react as a base has something to do with it.

You can make ammonia and sodium hydroxide solutions both with pH 11, but the sodium hydroxide solution is only 0.001 molar and thus cannot react with much oil on the skin.  Ammonia solution has a lot more base available to react with those fatty acids.  The weak base "hides" most of its reactivity in water alone but reveals when there are fatty acids to neutralize, so it's slip sliding away.

Probably anything that we consider basic and is sufficiently concentrated will slip in the fingers.