Object pose estimation is a fundamental problem in robotics and computer vision, yet it remains challenging due to partial observability, occlusions, and object symmetries, which inevitably lead to pose ambiguity and multiple hypotheses consistent with the same observation. While deterministic deep networks achieve impressive performance under well-constrained conditions, they are often overconfident and fail to capture the multi-modality of the underlying pose distribution. To address these challenges, we propose a novel probabilistic framework that leverages flow matching on the SE(3) manifold for estimating 6D object pose distributions. Unlike existing methods that regress a single deterministic output, our approach models the full pose distribution with a sample-based estimate and enables reasoning about uncertainty in ambiguous cases such as symmetric objects or severe occlusions. We achieve state-of-the-art results on Real275, YCB-V, and LM-O, and demonstrate how our sample-based pose estimates can be leveraged in downstream robotic manipulation tasks such as active perception for disambiguating uncertain viewpoints or guiding grasp synthesis in an uncertainty-aware manner.