Question

What is the SI unit for kinetic energy

Answer 1

The SI unit for kinetic energy is joules. Joules is measured in mass which is measured in kilograms.

Answer 2

The easiest way to build a unit for energy is to remember that
'work' is energy, and  
                                       Work = (force) x (distance).

So energy is                   (unit of force) x (unit of distance)

                   [Energy]  =       (Newton)            (meter) .

'Newton' itself is a combination of base units, so
energy is really
                             (kilogram-meter/sec²)      (meter)

                       =           kilogram-meter² / sec² .

That unit is so complicated that it's been given a special,
shorter name:
                                       Joule .

It doesn't matter what kind of energy you're talking about.
Kinetic, potential, nuclear, electromagnetic, food, chemical,
muscle, wind, solar, steam ... they all boil down to Joules.

And if you generate, use, transfer, or consume 1 Joule of
energy every second, then we say that the 'power' is '1 watt'.