Having close-to-capacity performance and low error floor, even for small block lengths, make spatially coupled serially concatenated codes (SC-SCCs) a very promising class of codes. However, classical window decoding of SC-SCCs either limits the minimum block length or requires a large number of iterations, which increases the complexity and constrains the degree to which an SC-SCC decoder architecture can be parallelized. In this paper we propose jumping window decoding (JWD), an algorithmic modification to the scheduling of decoding such that it enables pipelined implementation of SC-SCCs decoder. Also, it provides flexibility in terms of block length and number of iterations and makes them independent of each other. Simulation results show that our scheme outperforms classical window decoding of both SC-SCCs and uncoupled SCCs, in terms of performance. Furthermore, we present a fully pipelined hardware architecture to realize JWD of SC-SCCs along with area estimates in 12nm technology for the respective case study.