It seems that the Flex SDK does not include sources (if such sources exists at all) for the classes in flash.* package and therefore function name auto completion does not work at all.
This is a really critical problem in practical use, specially for new Flex users.
I fully understand that fixing this problem is not a simple code-change, but would one of the following approaches be possible:
1) Generating the required sources (or rather, header style stubs) based on published API documentation
2) Contacting Adobe and convincing them that if they want Flex to be successful then producing/giving sufficient header files for getting the flash.* package auto completion to work is also in their best interest.
Thanks for considering.
Issue was resolved
Perhaps this issue could be closed and IDEA-43227 could be changed so that it would include this "brakes auto completion" in addition of "incorrect unresolved type" warning (the root cause is probably the same).