Flash has a good set of export options, but I think they’re marred by bad menu design choices and some confusing variations across versions and platforms. Publishing a SWF is straightforward enough, but if you’re exporting to video formats, there are some potential pitfalls to avoid.

Question 1. Are you working with non-interactive animation only—no Movie Clip symbols or ActionScript? Then export to a PNG image sequence. Sure, it may be tempting to skip the hassle of reassembling the resulting folder full of images in a program like After Effects or Final Cut. But this is the only way you’ll be guaranteed perfect frame accuracy (one image file for each frame on your timeline) and a working alpha channel, no matter what Flash version you’re using. In my experience, all versions, Windows and Mac alike, behave identically with this option.

However, if you do use Movie Clip symbols or ActionScript in your project, then your options depend on which Flash version you have.

Question 2. Do you use Flash 8 or earlier? Older versions have no built-in way of recording real-time events to video, which means Movie Clip symbols won’t display properly and ActionScript will be ignored. So you’ll need to publish to a SWF, then run the SWF and find a way to record the results. The simplest aproach is to use a screen-capture program like Snapz (USD $70, OS X) or Fraps ($40, Win).

You could also record out over analog video to a DV camera or similar device, but unless you have a specific reason to prefer this option, I wouldn’t recommend it—it’s a hassle to set up, and there are a lot more variables to contend with that could potentially affect image quality. A third alternative, also impractical for most purposes, is to set up a video camera on a tripod and record straight off your LCD monitor. (With a good camera and an experienced operator, this can be quite nice.) None of these methods, unfortunately, will preserve an alpha channel.

Question 3. Do you have Flash CS3 or later? In more recent versions, Adobe added a built-in screen capture option for recording realtime output, alpha channel included. Unfortunately, they made the terrible decision of hiding this important feature in the menu File / Export / Export Movie / Quicktime. In most other programs, a menu option like that will give you a frame-accurate copy of your project, and this is emphatically not the case here—remember, it’s a record of a real-time performance, not a rendering of each frame in your timeline. Why couldn’t they have just named it something else?