As is well-known, the moduli spaces of smooth flat \(G=SU(3)\) connections on the oriented 3-holed 2-sphere \(D\) with fixed holonomies along the three oriented boundary loops can be identified with the spaces \(\mathcal M_{D,\Theta}\), parametrized by \(\Theta\) in a triangular domain in the Lie algebra of a fixed maximal torus of \(G\). The paper studies carefully this identification and discusses the necessary and sufficient conditions for the moduli space to be non-empty. Based on representation theoretical data, the results distinguish only two nontrivial possibilities: either \(\mathcal M_{D,\Theta}\) is homeomorphic to the 2-sphere, or it is one point. Furthermore, the author studies the relationship to the \(\widehat{\mathfrak s\mathfrak l}(3;{\mathbb C})\) fusion rules and thus also the conditions for the non-triviality of the fusion coefficients are described. Finally, the fusion coefficient of a triplet of extremal highest weights equals always one, providing an analog to the classical PRV-conjecture.