The programming language for Adobe Flash is called "Actionscript". It is separated into Actionscript 1.0, 2.0, and 3.0. Each one has it's own unique features and for most users AS 1.0, and 2.0 suit the job perfectly fine.
Adobe's Actionscript language is owned by Adobe after being acquired from Macromedia in 2005. Actionscript is particular to Flash and is not used in any other major web programs that I am aware of.
Actionscript is the only other language that I program with for Flash and I do not use anything else. It is very flexible and has many uses for communicating with xml, databases, and other web dev apps/files.
If you WANT TO CREATE GOOD FLASH GAMES, you will NEED TO LEARN ACTIONSCRIPT. This is all it comes down to. Actionscript is much easier than Java and C++ I would say. It is just the visual twist that catches people off guard by having to program objects that you can visually see and you have to understand the connection between the object on the screen and the programming that is attached to it.