Adobe Flash is owned by Adobe and so there's no free and legal way to create flash content.
That said, there are one or two ways to create flash-like content but none that I see offer Flash's ActionScript programming for stuff like games. Buttons, simple animations, transitions and such only although Ididn't research this too far.
this problem has been around in my company also: the lisence is so expencive that we have to move the few lisenced versions from computer to computer and because we're a business there's really no way around...
Gah! I'm so stupid sometimes. Alright - most of the time.
The current version for creating Flash content is owned by Adobe but it was first owned and developed by Macromedia. As such, you can go to http://www.oldversion.com/program.php?n=flash to get a fairly old and less-developed (yet very functional) version for free.
If memory serves, Macromedia only took it as far as ActionScript 1.0 so it won't be quite as developed for programming but it's certainly going to give you 95% of the capabilities that you're looking for.