If you are not using Flash Builder go here: http://www.adobe.com/devnet/air/air-sdk-download.html
At the bottom it says:
Note : Flex users will need to download the original AIR SDK without the new compiler. Mac Windows.
Download the proper one for your OS and then extract it over your existing Flex SDK directory.
EDIT: Just read your post again and noticed you mentioned Flash Builder. In that case you want to follow these directions: http://helpx.adobe.com/flash-builder/kb/overlay-air-sdk-flash-builder.html and grab the version with the compiler at http://www.adobe.com/devnet/air/air-sdk-download.html
Yeah, so far I've learned that I can copy the non-compiler version over my Apache 4.9.1 SDK and that has worked ok so far.
Also, I can copy the compiler version over the FB eclipse plugin folder mentioned above and that seems to work.
So I hope that by doing both there's a good chance I'm running the latest AIR (need to see if I can find a method I can call to verify the version of AIR I'm using at runtime.)
Unfortunately, I'm still not having any luck accessing my native android resources. I'm going to have to dig through more of the open source ANE's out there to see if one actually makes resource calls - the 2 I've viewed so far don't use them.