Personally, I think flash on web sites is overused (or used poorly) and usually gets in the way of what you have a website for, which is to market you and your work (not show off the website designer's skills).
Why does using it work against you? In the past, using a lot of flash on a website was considered SEO suicide. That just means that all the flash on websites was invisible to the search engines and not good for SEO (Search Engine Optimization). These days it's getting better, search engines and SEOs have continued to work on ways to help flash webpages be more recongnizable to the search engines. But it's early in that game, which means a lot of added cost to you if you really must have it. And if you must, just consider that part of the site invisible (as far as SEO is concerned) and make sure you have your critical info and anything important you want to say as part of a regular (html) web page.