Transformer-based models dominate modern AI workloads but exacerbate memory bottlenecks due to their quadratic attention complexity and ever-growing model sizes. Existing accelerators, such as Groq and Cerebras, mitigate off-chip traffic with large on-chip caches, while algorithmic innovations such as FlashAttention fuse operators to avoid materializing large attention matrices. However, as off-chip traffic decreases, our measurements show that on-chip SRAM accesses account for over 60% of energy in long-sequence workloads, making cache access the new bottleneck. We propose 3D-Flow, a hybrid-bonded, 3D-stacked spatial accelerator that enables register-to-register communication across vertically partitioned PE tiers. Unlike 2D multi-array architectures limited by NoC-based router-to-router transfers, 3D-Flow leverages sub-10 um vertical TSVs to sustain cycle-level operator pipelining with minimal overhead. On top of this architecture, we design 3D-FlashAttention, a fine-grained scheduling method that balances latency across tiers, forming a bubble-free vertical dataflow without on-chip SRAM roundtrips. Evaluations on Transformer workloads (OPT and QWEN models) show that our 3D spatial accelerator reduces 46-93% energy consumption and achieves 1.4x-7.6x speedups compared to state-of-the-art 2D and 3D designs.