Dialogue flows are high-level representations of the possible interactions in collections of dialogue. They have several applications, but are rarely available and often produced manually. We optimise dialogue flow discovery by leveraging dialogue act annotations in a collection of dialogues and apply the resulting configuration for discovering flows from additional collections. Moreover, for increased interpretability, we resort to an open large language model as a flexible approach for labelling the states of the discovered flows. To confirm the suitability of the adopted approach, discovered flows are presented, described and evaluated.