Provided are a computer program product, system, and method for generating a chain of a plurality of write requests including a commit wait flag and plurality of write requests. The commit wait flag is set to one of an indicated first value or a second value. The commit wait flag is set to the first value to cause a storage server to process the write requests by requiring a current write request being processed to complete before transferring data for a next write request following the current write request. The commit wait flag is set to the second value to cause the storage server to process the write requests by transferring data for the next write request before completing the current write request preceding the next write request. The write request chain is sent to the storage server to apply the write requests to the storage.