Building multiple microgrid (multi-MG) clusters is conducive to accessing high penetration of renewable generations, consuming electric energies locally, and reducing operating losses. Nevertheless, it causes a challenge that the interconnectivity of multi-MG clusters may be seriously affected by short-circuit faults. To figure out the issue, this paper puts forward a solution of using flux-coupling-type superconducting fault current limiters (SFCLs), which are positioned at the points of common coupling (PCCs) among the multi-MG clusters and the distribution system. Considering the power exchange and balance under faults, the interconnectivity characteristics of the multi-MG clusters are theoretically analyzed, and the potential actions of the SFCLs to boost the interconnectivity are expounded. Using MATLAB, a modified IEEE 13-node distribution system containing multi-MG clusters and flux-coupling-type SFCLs is modeled, and different fault scenarios are simulated to assess the efficacy and suitability of the proposed solution. From the findings, the SFCLs can very usefully relieve the power fluctuation and mitigate the PCC voltage drop for the multi-MG clusters. Not only the operation of tripping off the multi-MG clusters is efficaciously avoided, but also a stronger power support capability withstanding the fault rush is appreciatively obtained.