I use Camtasia for doing screen recording (and Camtasia Studio for editing). It's a not-inexpensive product that I happen to own for a project I did for a client a couple of years ago. The screen recorder is excellent and the editor is pretty decent, if not nearly as sophisticated as something like Adobe After Effects.
Getting Foreflight to appear as an overlay took only a tiny bit of work, really. I started with a product called "AirServer" (see
http://www.airserver.com) that allows you to mirror your ipad (or an iphone, I guess) to a Mac or PC display using AirPlay. It's a very nice product -- less than $20 for a 5-PC personal license and it works great. I set that up on one of my external display PC's (I fly a more-than-usually complex sim -- I have 6 PC's that make up the full simulator, driving multiple external displays). In this case, I took up space on my 90-degree left display to mirror the iPad running Foreflight. Then, I started the Camtasia recorder on both systems at roughly the same time, then did the flight. Afterwards I used Camtasia Studio's editor to import both the flight video and the ForeFlight video, and then resized the Foreflight overlay to make it a bit smaller and to show on top of the "flight" video.
I'll note that you don't need a complex setup like mine to pull this same sort of thing off -- you could use a laptop alongside your flight simulator setup, even if it's only a single PC to run AirServer and as long as you've got some kind of screen video capture application (Jing, or SnagIt from TechSmith's for example if you don't have something fancier like Camtasia), you can record both the screen on your flight sim and the screen on your laptop at the same time.
There is actually a screen recorder that lets you simultaneously record multiple regions of your screen (or screens if you have multiple monitors) called 'XSplit', but even with an overclocked i7 quad-core CPU I couldn't run XSplit and maintain good framerates on FSX, hence my decision to take the approach I did.
-M.