FPGAs are increasingly gaining traction in cloud and edge computing environments due to their hardware flexibility, low latency, and low energy consumption. However, the existing hardware stack of FPGA and the host-FPGA connectivity does not allow flexible scaling and simultaneous reconfiguration of multiple devices, which limits the adoption of FPGA at scale. In this paper, we present SAF -- an Ethernet-based scalable acceleration framework that allows FPGA to be hot-plugged into a network in a stand-alone fashion without connecting to a local host CPU, which enables flexible scalability. SAF provides a custom FPGA shell and a set of Ethernet protocols that allow FPGAs to connect with a remote host to accelerate application kernels. SAF can configure multiple FPGAs simultaneously, which significantly reduces the reconfiguration time in scaling effort. We implemented the SAF framework using Intel FPGA SDK for OpenCL and 20 Bittware 385A cards with Arria-10 FPGAs. We analyze a case study and conduct experiments to compare SAF with state-of-the-art multi-FPGA clusters. Results show that SAF provides 13X faster reconfiguration than sequential PCIe programming, reduces the hardware setup costs by 38%, application runtime by 25%, and energy consumption by 27%. We evaluated the performance scalability of SAF using the PTRANS benchmark of the HPCC FPGA benchmark suite and showed an almost linear speedup for strong and weak scaling scenarios.