I found a way to do this. Basically you need to configure the LeanFT Extension to allow Incognito mode. Then in your code, launch Chrome as usual and perform DeviceReplay steps to open an Incognito browser. Close the original browser, and attach the new incognito browser.

• Open Chrome
• Manually go to Tools>More Tools>Extensions
• Click Details for Micro Focus Functional Testing Agent
• Enable "Allow in incognito"
• This code uses key codes like DeviceReplay (https://testguild.com/qtp-code-devicereplay-presskey/) or KM184330 and KM1194127

var browser = BrowserFactory.Launch(BrowserType.Chrome);
Keyboard.KeyDown(157); //hold down Control key
Keyboard.KeyDown(42); //hold down Shift key
Keyboard.PressKey(49); //press N
Keyboard.KeyUp(157); //release Control key
Keyboard.KeyUp(42); //release Shift key

browser.Close(); //Close original browser

//Attach new incongnito browser
var IncogChrome = BrowserFactory.Attach(new BrowserDescription
{
Title = "New Tab"
});

//Do test stuff
IncogChrome.Navigate("http://google.com");

var search = IncogChrome.Describe<IEditField>(new EditFieldDescription
{
Name = @"q"
});
search.SetValue("Orasi Software");
var googleSearchButton = IncogChrome.Describe<IButton>(new ButtonDescription
{
AccessibilityName = @"Google Search",
ButtonType = @"submit",
Name = @"Google Search",
Role = string.Empty,
TagName = @"INPUT",
Index = 1
});
googleSearchButton.Click();

var link = IncogChrome.Describe<ILink>(new LinkDescription
{
InnerText = @"Home - Orasi Software Incorporatedhttps://www.orasi.com",
TagName = @"A"
});
link.Click();
IncogChrome.Close();