Fire segmentation remains a critical challenge in computer vision due to flames' irregular boundaries, translucent edges, and highly variable intensities. While the Segment Anything Models (SAM and SAM2) have demonstrated impressive cross-domain generalization capabilities, their effectiveness in fire segmentation -- particularly under mobile deployment constraints -- remains largely unexplored. This paper presents the first comprehensive evaluation of SAM2 variants for fire segmentation, focusing on bounding box prompting strategies to enhance deployment feasibility. We systematically evaluate four SAM2.1 variants (tiny, small, base_plus, large) alongside mobile-oriented variants (TinySAM, MobileSAM) across three fire datasets using multiple prompting strategies: automatic, single positive point (SP), single positive point + single negative point (SP+SN), multiple positive points (MP), bounding box (Box), and hybrid variants (Box+SP and Box+MP). Our experimental results demonstrate that bounding box prompts consistently outperform automatic and single point-based approaches, with Box+MP achieving the highest mean IoU (0.64) and Dice coefficient (0.75) on the Khan dataset. Lightweight variants such as TinySAM and MobileSAM further reduce memory and computational costs, making them more suitable for latency-tolerant edge scenarios. Overall, this work provides critical insights for deploying promptable segmentation models in fire monitoring systems and establishes benchmarks for future research in domain-specific SAM applications. Code is available at: https://github.com/UEmmanuel5/ProFSAM