The integration of serverless computing with edge environments introduces a paradigm of highly distributed, low-latency processing. However, orchestrating complex serverless workflows across a heterogeneous continuum of resource-constrained edge devices and powerful cloud nodes presents significant challenges in latency, state synchronization, and fault tolerance. Existing orchestration systems, often designed for homogeneous cloud environments, struggle with the inherent network instability and resource asymmetry of edge-cloud topologies. This paper presents FlowMesh, a dynamic service mesh architecture specifically designed for decentralized serverless workflow orchestration. FlowMesh introduces a novel, lightweight control plane that embeds orchestration logic directly within a mesh of sidecar proxies co-located with function runtime environments. This design enables intelligent, context-aware routing and state management without a centralized bottleneck. Key innovations include a distributed consensus protocol for fault-tolerant state management, a latency-aware function placement scheduler, and a transparent checkpointing mechanism for seamless fault recovery across stateful workflows. We evaluate FlowMesh against state-of-the-art systems, such as FaaSFlow and AWS Step Functions, in a simulated edge-cloud testbed. Results demonstrate that FlowMesh reduces end-to-end workflow latency by up to 40% in edge scenarios and improves fault recovery success rate by 65% compared to cloud-centric alternatives, while maintaining minimal overhead. This work provides a blueprint for building robust, high-performance serverless platforms that truly span the edge-to-cloud continuum.