I am working with a web-page or a user-script (It's not about chrome extension) and as per my requirement i wants to open incognito mode.
Here is my JavaScript Code:
$('#google_alert').on('click', function(e)
{
    swal({
        title: "Review Us",
        text: "You will be redirected to review us on google",
        type: "warning",
        showCancelButton: true,
        confirmButtonColor: "#09a275",
        confirmButtonText: "Positive",
        cancelButtonText: "Negative",
        closeOnConfirm: false,
        closeOnCancel: true
    }, function(isConfirm)
    {
        if(isConfirm)
        {
            chrome.windows.create({"url": "http://www.google.com", "incognito": true});
        swal("Thank you", "Thank you reviewing us.", "success");
        }
        else
        {
            $("#review-modal").modal('show');
        }
    });
    return false;
});
Response: ReferenceError: chrome is not defined
Here is procedure of what i am doing,
- click on google review option on web page,
 - it will redirect user to google review page,
 - google ask to login,
 - user enter credential and provide review,
 - back to web page.
 
Here you can see that no need to save user's ID and passwords into browser.