Firefox coming on April 2013 to natively allows you to open any link in private window from context menu.  Mozilla has finally added most requested feature, per-window private browsing to Firefox 20 nightly builds which are now available for testing for Windows, Mac and Linux. Do you know: apart from opening new private browsing window without closing the current session Firefox also allows you to open any link in a new private window, for that all you need to do is right click on any link and select “open link in New Private Window”.

Until Firefox 20 releases officially you can use “Open In Private Browsing Mode” add-on to open links in private browsing mode from right click menu in Firefox.

Firefox 20 gets the ability to open link in private browsing window from context menu

You can test this feature by downloading Firefox nightly build from here.