It's not possible to configure the export function of vscode-jupyter by extra command line arguments passed to nbconvert. The feature request microsoft/vscode-jupyter#13918 was declined.

A workaround is to specify additional arguments in a configuration file jupyter_nbconvert_config.py in the .jupyter folder (its location can be shown by python.exe -m jupyter --path).

Contents of jupyter_nbconvert_config.py to hide prompts (equivalent to --no-prompt):

c = get_config()

c.TemplateExporter.exclude_input_prompt = True
c.TemplateExporter.exclude_output_prompt = True