The authors consider three parameter families of vector fields on \(\mathbb{R}^3\) that unfold an inclination flip homoclinic orbit of weak type. The singularity to which the homoclinic orbit converges has three distinct real eigenvalues. Denote these eigenvalues by \(- \alpha\), \(- \beta\) and 1 with \(\alpha > \beta > 0\) (after time rescaling). It is assumed that \(1/2 < \beta < \alpha < 1\). In this case the two dimensional stable manifold contains a unique \(C^2\) weak stable manifold. An inclination flip homoclinic orbit is of weak type if it is contained in this \(C^2\) weak stable manifold. This defines a homoclinic bifurcation of codimension three. The authors prove the existence of inclination flips of \(n\)-homoclinic orbits, for all \(n\), branching from the codimension three bifurcation point.