Does there exist the method of projective coordinates for the computation of scalar multiplication for Koblitz curve?
Koblitz curves are still (convertible to) elliptic curves with a short Weierstrass equation.

Therefore you can use the standard projective / Jacobian coordinate systems as you'd use for more generic curves, though I think (variants of) Jacobian coordinates tend to perform best. All of these coordinate systems only require a single modular inversion at the end of the scalar multiplication, in an operation often called "rescaling".

If your curve is additionally of the form $y^2=x^3+b$ further optimizations seem to be possible using a special case of Jacobian coordinates.