Current and Electrons

Why is flow of current visible in form of spark/discharge, contrary to
flow of current in a wire?

Because sparks and discharges occur when the electrons are accelerated
by very high voltages, have therefore very high energies, and are hence able to ionize (or at least excite) gas atoms. When these atoms recombine (or get de-excited), light is released. What you see is that light.

In contrast, the electrons forming the current in wire have in general very low energies (rough estimate: the energy is at least a factor 1000 lower).

(1) Electrons forming the current in wire is not enough to ionize atoms or even cause much excitations,

(2) even the small excitations which are nevertheless caused don't release very much energy when the atoms get de-excited, and therefore no visible light, but at best infrared radiation, and

(3) wires are obviously not transparent, so even if light was created in the wire, you would not see it from outside.

Electrons can't be seen because, they are smaller than the wavelength of visible light.