Flashback is extinct and hasn't been see for over a year now. When it was active there was never any proof that it passed on any private information from the computer, it just redirected your browser to advertising sites. Don't give it another thought.
The topic being discussed here is "Cannot download Java SE6 plug in". If that's not your problem, then you need to start with a new topic and describe what it is. That way you will get a lot more help than trying to change the subject here.
If you just want to know how to keep safe, then follow Apple's instructions to keep Java disabled in all your browsers except when you must visit a site that requires it's use. Make sure you disable it again before you leave that site. Also make sure to use Software Update to keep Java, your OS and all Apple apps fully up-to-date. You posted to an OS X 10.6 Snow Leopard forum, so I assume that's what you are currently using. There have been indications this week that Apple will no longer support your OS with even critical updates, so if you are able to upgrade your OS, you should do so very soon.