Kirigami-inspired designs can enable self-folding three-dimensional materials from flat, two-dimensional sheets. Hierarchical designs of connected levels increase the diversity of possible target structures, yet they can lead to longer folding times in the presence of fluctuations. Here, we study the effect of rotational coupling between levels on the self-folding of two-level kirigami designs driven by thermal noise in a fluid. Naturally present due to hydrodynamic resistance, we find that this coupling parameter can significantly impact a structure's self-folding pathway, thus enabling us to assess the quality of a kirigami design and the possibility for its optimization in terms of its folding rate and yield.