Head over to Flash Game Dojo's Getting Started page, they'll walk you through getting all your tools downloaded and installed.
Step 2: Make a Game!
Hello World is always a good place to start - here are thorough tutorials for FlashDevelop and Flash Builder. You can hit up Flash Game Dojo's online knowledge base or check out these sample open source projects:

Step 3: Share it
The best thing about making a Flash game is that almost everyone with a computer can play it. Upload your game to Flash Game Dojo so you can share it with the rest of the world!
Display Hundreds of Objects at Once
Create Tilemaps from Text Files or Images
Generate and Emit Particles for Hot Effects
Play Positional, Streaming, Looping Sounds
Scroll Objects or Groups in Parallax




