If a LC circuit is considered analogous to a harmonically oscillating spring-block system, which energy of the LC circuit would be analogous to potential energy and which one analogous to kinetic energy?

We are considering the LC circuit as analogous to harmonically oscillating spring block system.

In LC circuit

Magnetic energy =

Magnetic energy is needed to produce current through the inductor.

Electric energy =

Electric energy is required to made the electron to be in the motion. Then current will flow. So it is related to potential energy.

Current means movement of electrons (flow of electrons). So magnetic energy is related to kinetic energy.