I frequently see young fledging artists and businesses using Flash to make a fancy- looking website thinking it will allow them to play in the big leagues, and set them apart from your average upstart. But this strategy is like playing in a beautiful stadium with no-one in the audience.
Here’s some reasons why that can be a Very Bad Idea:
1)    Flash is hard to properly optimize for search engines. While there have been some advances by the search engines in this area, you will not be able to optimize your site in the depth and detail that you can an HTML site.

2)    This means that, sure your site might come up first in Google if someone types in your company name, but that means they are already looking for you and aware of you. What about all the potential visitors you miss out on because your site does NOT rank for a slew of other related keyphrases?

3)    With an HTML site you can optimize each page according to its content, for different phrases/words – this is the best way to do it. Flash does not allow you to do this – essentially your homepage will be indexed but not much else.

4)    When you are a new artist/business looking to raise awareness and expand your target audience, you need to make yourself as accessible as possible to targeted traffic, and that means SEO in addition to other promotional avenues. Don’t make an already uphill battle even harder by starting out with a Flash-site that immediately limits your audience.

5)    Because of all the above, your organic search traffic will be relatively low, at least to start out with, leaving you to rely on other methods to get traffic, such as your own promotional abilities to spread the word, slugging away on Facebook etc.

6)    Loading pages, especially when they take too long are an obstacle to people getting to the good stuff. You risk losing people before they even see your site, never to return. And if you do get repeat visitors, it’s a bit annoying to have to wait for the site to load every time.
My personal advice for using Flash is to limit it to adding cool, but functional design features or flourishes, but not to build an entire site only in Flash.

It’s easier for well-known brands to use Flash, or even sites that are very text-light, and still rank highly because they receive a lot of incoming links from many other sites which helps them compensate for the lack of text on their own site. Using an example I saw on an old post at SEOBook.com, we can see this demonstrated in a search for “coffee” or “chocolate”. At the time that post was written, Starbucks ranked #1 in a search for ‘coffee’ despite having very little text on their site, and Hershey’s and Godiva ranked top in the chocolate search. This was attributed to the amount of incoming links for these brands which proved them to be relevant. These brands still rank highly today, but in both cases the #1 spot is now taken by pages on the distinctly un-flashy Wikipedia.

If you have a Flash site already, there are numerous articles that get pretty technical about SEO for Flash and since Flash isn’t my area of expertise I’ll leave it to them to explain how you can make the most of what you’ve got:
How To SEO Flash
A Modern Approach To Flash SEO
SEO Friendly Flash
Does Flash SEO Still Suck?
Improved Flash Indexing