How much might soft skin reduce aircraft skin friction?
This has mostly been examined for aquatic flow, e.g. with the soft skin of dolphins. Studies were done with test setups because measuring the boundary layer around live dolphins is exceedingly hard.

One study compared a rigid cylinder with a soft one of the same dimensions, using a polyurethane coating. Below is a diagram from that study with 3 denoting the rigid and 6 the soft cylinder. As you can see, the difference is small but consistent over the range of Reynolds numbers tested. Picture source here.



For dolphins, active regulation of muscle tension might be responsible for a resonant vibration of the skin, but much of the literature is still rather speculative. From the study:


  Based on experimental research on live dolphins, a hypothesis has been formulated (see Chapter 1); this is that by the regulation of the skin muscle tension dolphins promote resonant interaction with a flow. This leads to interaction of fluctuations of the boundary layer and natural frequency of fluctuation of the dolphin skin. As a result, the skin coverings vibrate with resonant frequency practically without energy consumption. Fluctuations of this coating occur at a frequency that controls the frequency of bursting from the viscous sublayer. This is also the reason for the abnormally low resistance, which has been discovered in the authors’ modeling experiments.