The emerging reconfigurable circuit technology, which can establish circuit connections among switches, has been proposed as a promising paradigm for datacenter networks. This paper investigates how to accelerate the non-preemptive multicast flows in a demand-aware manner in reconfigurable datacenter networks. Firstly, the problem of scheduling the circuit switch to minimize the average completion time is introduced and proved to be NP-hard. A two-round matching algorithm is proposed to handle the conflicts between different multicast flows under the bandwidth constraint. The approximation ratio of the proposed algorithm is proved to be $2\sqrt {2n} $, where n denotes the number of Top-of-Rack (ToR). Finally, we have demonstrated that the proposed algorithm can effectively reduce the average completion time of the flow compared to state-of-the-art algorithms through extensive simulations.