Flash has traditionally not been a very translation-friendly format. It was difficult to get to the text if you didn't have a copy of the expensive Adobe (formerly: Macromedia) Flash Professional. Any Flash source file (*.fla) created from Flash Professional CS5 on (the current version is CS6) follows the same structure that many other file formats use: it's actually a compressed file that contains XML files which in turn contain the translatable text. All you need to do is rename the *.fla file to a *.zip file and unzip it (leaving the folder structure intact), locate the *.xml files with the translatable text and translate them (in a text editor or, even better, in a translation environment tool), place the translated *.xml files in their original folder, zip the whole folder structure up again, rename from *.zip to *.fla, and you're done. This of course presupposes that the creator of the Flash file knew what s/he was doing and created an internationalization-ready file rather than having text sit in images, for example.
Jost Zetzsche, A computer newsletter for translation professionals, Issue 13-4-221 (the two hundred twenty-first edition)