For those of you who are interested in always launching Brave browser in default incognito mode. Here are the steps.
Touch and hold Brave icon on your home screen.
You will get popup with 2 options… New tab = and New incognito tab =.
Touch and hold on New incognito tab = to create a new incognito shortcut on your home screen.
Every time when you tap Brave incognito shortcut from here, it will open in default incognito (private browsing) mode.
I hope the Brave browser developer can also look into the possibility of launching external links (e.g. links from Whatsapp and SMS) with Brave browser in default incognito mode as well. At present, I can’t seem to find a way to do it.