You seem to suggest that RIA development implies Flash/Flex development.
However, applications like GMail and Google Maps have long shown the world that rich experiences can come from AJAX as well.
Also, with HTML5 coming our way, I expect Flash dev roles to gradually die down.
If at all possible, I'd try to get away from this proprietary technology and move onto open standards, i.e. AJAX.
I am also assuming that you are specialising in front-end development. I would therefore try to learn more about the back-end, say databases or newer technologies like distributed caches or NoSQL. Know nothing about Unix? Explore it. Experiment. Basically my recommendation on your way to becoming an architect is to "get out more", in other words avoid the mistake I made earlier in my career, becoming highly specialised in one technology, while neglecting everything else around it.
Not sure what courses there are around that would cover this stuff though. Also what you can sell to your bosses depends on how competent (and the fact that they are presumably the ones that chose Flash as a front-end and the fact that they recommend an "architect" course doesn't leave me with high hopes) and open-minded they are.
Depending on your company's sector (e.g. pharmaceutical), you may also want to learn more about the business, too. Having said that, most IT knowledge is portable across businesses, whereas business knowledge by definition is not.
Another factor is how much you like your company and how amenable you would be to moving onto greener pastures in a couple of years' time.