There are so many programs around to make Flash files it's silly, but to upload them to Armor Games you need a copy of Flash (preferably the latest version - Flash CS4) which is an IDE made by Adobe. That will be . . . Ehm, $699 please. It also comes with animation tools and in-built art thing as far as I know.
You can also use FlashDevelop, I'm not sure if you can upload games using FlashDevelop to Armor Games, but it's free and you still learn how to program in Flash. If you want to see if programming games is something you want to do, download the free trial for Adobe Flash CS5 or FlashDevelop.
For art you can use GIMP or Photoshop. I'd advise GIMP since I doubt you have ~$1, 400 to spend on making Flash games.
Probably want to wait until you get someone with more expertise to tell you whether or not FlashDevelop does work with Armor Games - I'm pretty sure it saves files in the same swf format - the most popular thing to make games with around here though is Flash CS5.
