Preamble: I’m a huge fan of Alfred App. This post isn’t about Alfred per se, but if you’re a Mac user, do yourself a favour and grab a copy. There’s a free version, and the “powerpack”. The powerpack is what is needed to follow the rest of this post.
Years ago I wrote Launching your browsers in Private Mode with Alfred as a quick little Alfred extension. I was recently asked if I’d updated the extension for Alfred 2. Sadly, I had not, but a quick search showed that someone else had already done the grunt work on the Alfred forums, which I’ve backed up here (you may need to right-click ‘save link as’) to ensure the workflow will always be available.