A storage system comprises a shared storage environment that includes a storage array having at least one storage volume shared between first and second host devices. The storage system further comprises a server associated with the storage array, at least first and second clients associated with the respective first and second host devices, and a first block cache arranged between the first client and the storage array. The server is configured to coordinate operations of the first and second clients relating to the storage volume shared between the first and second host devices in a manner that ensures coherency of data stored in the first block cache. The server may comprise a storage block mapping protocol (SBMP) server and the first and second clients may comprise respective SBMP clients. The block cache is illustratively implemented using a VFCache or other type of server flash cache.