It's pretty simple. 

The formal definition of velocity is the derivative of position with respect to time. So in one dimension:

$v = \frac{dx}{dt}$

And therefore

$x(t) = \int_{0}^{t}v(t')dt'$

If you assume $v(t)$ is constant, then that equation becomes $x = vt$ (hence the kinematic equation). If $v(t)$ isn't constant, then $x=vt$ is almost certainly not correct.