What kilogram is doing in volt unit definition?
It's part of the Force. Well, just force actually. Which is mass times acceleration.

\$\mathrm{V=\dfrac{J}{C}}\$

\$\mathrm{J = N\cdot m}\$

\$\mathrm{N = \dfrac{kg\cdot m}{s^2}}\$

\$\mathrm{C = A\cdot s}\$