The work done by kinetic friction on an object is always negative.
False
Consider the situation where a block is in a train and a force is applied such that it is sliding against friction with constant velocity. We know its velocity and displacement will be in the +ve x direction.
Now let us say the train starts moving in the -ve x direction with a velocity greater than the velocity of the block.
Now from the ground frame the velocity of the block will be in the -ve x direction and kinetic friction will be doing positive work.