@swingliner the career portion has more to do with being able to formulate and execute designs than the technologies used. If Flash offers what you need to create the site of your dreams, then use it. It is still the standard way to get animation on the web and studios and individuals can certainly make a career of being proficient in Flash. (2advanced Studios and Paul Neave for example will always find work)
What makes their work stand out though is that it’s well thought out and uses the strengths of the technology (flash) while minimizing the shortcomings (file size, slow loading, tendency towards concentrating on effects rather than effective presentation)
I’m way off track here, your question is where do you start. Well, do you have the software to make Flash movies? If not you’ll need to get a copy of Adobe Flash, the newer the better but really whatever you can afford. You may want to go ahead and get a copy of an Adobe Creative Suite so you’ll have some of the supporting programs like Photoshop (or Fireworks) and Illustrator that you’ll use to create graphics for your site. (a recent discussion on student copies of the various software may help)
Once you have the software, it really depends on how you learn best where to go from there. I’m always most motivated if I have an idea in mind and want then learn how to create that particular idea. I would dream up a site that did some of the things I wanted to learn and then go through piece by piece to learn those parts. If you know some HTML, that will help. Maybe grab a book on Flash so at least you have some lessons to get the basics down. The Adobe website also has a number of tutorials that start with no assumption of prior knowledge, so start there if you don’t want to drop cash on a book right away.
Will you be turning out great work in 30 days like some of the books claim, probably not. But the key to making great sites seems to be just keep making sites and learn a little bit on each one. As long as you don’t start just falling back completely on what you know you’ll progress and get better. Give it a shot, the 5 or 6 years you mention is a lifetime for designing on the web right now. Styles changes pretty fast. If you constantly have a least one project you’re working on, you’ll probably be surprised how quickly you develop your own style and skill set slanted towards the types of projects you want to do.
Above all, enjoy it and good luck.