Space information network (SIN) can provide global coverage in 6G network. Furthermore, SIN with network function virtualization (NFV) can achieve flexible deployment of network functions and improve the utilization of resources. In SIN with NFV, network functions can be virtualized into virtual network functions (VNFs). However, in SIN with NFV, the mission flow must satisfy the service function chain (SFC) constraint, i.e., the mission flow must be processed by all VNFs in the predefined order. Furthermore, each VNF can be deployed on multiple physical nodes. Moreover, different kinds of services may have the diverse quality of service (QoS) requirements. In this paper, we investigate the joint VNFs deployment and flow routing strategy (VNF-R) to maximize the number of completed missions with the guaranteed end-to-end latency under SFC constraints in time-varying SINs. Specifically, the problem can be formulated as a mixed integer linear programming (MILP) problem, which is proved to be NP-hard. In order to effectively solve the problem, we propose a novel low-complexity near-optimal penalty successive upper bound minimization rounding LP relaxation iterative rounding (PSUM-R-LRIR) algorithm. The simulation results show that the PSUM-R-LRIR algorithm can achieve near-optimal performance, and our proposed VNF-R scheme significantly outperforms the fixed VNF deployment scheme.