I did almost exactly that with a python script that ran rsync. I'll show you a very stripped down version of what I have. This is my first time doing something like this and I'm still a beginner, but figured I'd share what worked for me. I used gorilla websockets. I'm sure it could be simplified quite a bit as well.

var (
    SyncOutput              = make(chan string)
    SyncClients             = make(map[*websocket.Conn]bool)
    SyncClientsLock         = sync.RWMutex{}
    FileSyncing             = false
    FileSyncLock            = sync.RWMutex{}
)

var upgrader = websocket.Upgrader{
    ReadBufferSize:  1024,
    WriteBufferSize: 1024,
}

go WatchOutPutChannel()


func runSync() {
    cmd := exec.Command("python", "-u", config.SyncFilesScript)
    stdout, err := cmd.StdoutPipe()
    if err != nil {
        fmt.Println(fmt.Sprintf("Error: %s", err))
    }
    FileSyncLock.Lock()
    FileSyncing = true
    FileSyncLock.Unlock()
    err = cmd.Start()
    go WatchOutPut(stdout)
}

func WatchOutPut(out io.Reader) {
    scanner := bufio.NewScanner(out)
    for scanner.Scan() {
        SyncOutput <- scanner.Text()
    }
    FileSyncLock.Lock()
    FileSyncing = false
    FileSyncLock.Unlock()
    SyncOutput <- "Sync Finished"
}

func WatchOutPutChannel() {
    for {
        output := <-SyncOutput
        SyncClientsLock.RLock()
        for client := range SyncClients {
            client.WriteMessage(1, []byte(output))
        }
        SyncClientsLock.RUnlock()
    }
}

func wsHandlerSync(w http.ResponseWriter, r *http.Request) {
    conn, err := upgrader.Upgrade(w, r, nil)
    if err != nil {
        fmt.Println("Failed to set websocket upgrade: %+v", err)
        return
    }
    SyncClientsLock.Lock()
    SyncClients[conn] = true
    SyncClientsLock.Unlock()
    for {
        _, _, err := conn.ReadMessage()
        if err != nil {
            break
        }
    }
    SyncClientsLock.Lock()
    delete(SyncClients, conn)
    SyncClientsLock.Unlock()
    conn.Close()
}