It really depends on the type of app you are building. I have in the past used flash to create a video conversion app by piggy-backin on top of ffmpeg. (so really it was ffmpeg doing the actual conversion work) But it was my flash app that allowed people to drag and drop the file and select the output format etc.
Basically I built my app using flash and compiled it using Zinc 2.5. So basically all the functional was done in AS but again, the actual performing of the conversion was done by the ffmpeg binary based on the commands sent to it from the flash app.