Both are nouns, and both mean the "the quality of being friendly, generous, and considerate."
If you're speaking of an act, you could say "it was a kindness I'll never forget". But, you would probably never hear anyone say "it was a kindliness I'll never forget."
In Agatha Christie's A Holiday for Murder (part III section XIII) Hercule Poirot says of another character, "her steady hazel eyes . . . shone out like beacons of kindliness." Two sentences later she writes, "Colonel Johnson was talking in his kindliest tone."