We present \textbf{Flash-GMM}, a fused Triton kernel for efficient computation of Gaussian Mixture Models (GMMs) over large-scale data in a single GPU pass. By eliminating the need to materialize the full responsibility matrix in GPU memory, Flash-GMM achieves a \textbf{20$\times$} speedup over existing implementations and enables training on datasets more than \textbf{100$\times$} larger than previously feasible on one device. To demonstrate its impact, we integrate Flash-GMM into the IVF coarse quantizer for approximate nearest-neighbor (ANN) search. We show that soft GMM clustering is now a viable drop-in replacement for $k$-means, and that GMM responsibilities can be leveraged to assign border vectors to multiple clusters. Our approach reaches fixed recall targets with up to $1.7\times$ fewer distance computations, or equivalently, yields $+2$--$12$ recall@10 at matched computational cost. We release the kernel as an open-source project.