Flex Builder, the official IDE can be downloaded from here. It’s an Eclipse based tool you can either get as a plugin if you’re already using Eclipse or as a custom Eclipse build.
The downside is that you only get a sixty day trial for free unless you qualify for the education license terms. Adobe has also recently allowed unemployed developers to use Flex Builder for free with similar limitations to the educational license. You can find out more about that program here
You don’t have to use Flex Builder though. You can download the SDK from here and use your favourite editor and compile from the command line. If you decide to go that way, I suggest you check out the Google Maps Flex API docs for a useful tutorial.
An alternative free IDE (for Windows anyway – it’s built on a Visual Studio shell) is FlashDevelop. I’ve started using this since my trial expired and so far I like it. I’ll write another post on how to setup and use it.
A good place to start for websites is the Adobe Flex Developer site.