I am using Save and Run vscode extension for syncing code between local and remote server whenever I hit save in VSCode. Following is the configuration I am using.
"saveAndRun": {
  "commands": [
    {
      "match": ".*",
      "cmd": "rsync -av --no-owner ${file} {destination folder}${relativeFile}",
      "useShortcut": false,
      "silent": false
    },
  ]
}

The output generated when the rsync command is run can been seen in VSCode terminal. You can add the above configuration in .vscode/settings.json file. You can learn more about editing settings.json file here