Generative models have achieved remarkable success across various applications, driving the demand for multi-GPU computing. Inter-GPU communication becomes a bottleneck in multi-GPU computing systems, particularly on consumer-grade GPUs. By exploiting concurrent hardware execution, overlapping computation and communication latency becomes an effective technique for mitigating the communication overhead. We identify that an efficient and adaptable overlapping design should satisfy (1) tile-wise overlapping to maximize the overlapping opportunity, (2) interference-free computation to maintain the original computational performance, and (3) communication agnosticism to reduce the development burden against varying communication primitives. Nevertheless, current designs fail to simultaneously optimize for all of those features. To address the issue, we propose FlashOverlap, which utilizes a novel signaling mechanism: when part of the output finishes, the computation kernel sends a signal to trigger the communication of that part, while continuing the computation of the remaining part (interference-free computation). Consequently, the communication of the finished part and the computation of the remaining part can be overlapped. On top of the signaling mechanism, FlashOverlap comprises two key components: (1) the determination of the signaling timing to boost the overlap efficiency (tile-wise overlapping), and (2) a pre-communication reordering to create the contiguous address for finished data, enabling communication by simply calling NCCL APIs (communication agnosticism), and a post-communication reordering to correct the data order. Experiments show that FlashOverlap achieves up to 1.65x speedup through overlap, outperforming existing works in most cases. Code is available at https://github.com/infinigence/FlashOverlap.