Yes, you can add flash elements to a Wordpress theme, obviously if it's something like navigation you won't be able to have it update through WP (EDIT: Sounds like you can, as per Chris' reply below, but sounds tricky!) but other individual flash elements shouldn't be a problem.
The only way to fully (and very painfully) implement Flash and Wordpress completely (and at great length) is to use a program called Flex which makes DB ready flash web applications.. Its very long winded and uses MXML to do all the calls to the wordpress db, very interesting technology (which will be in with Flash CS5 from what i've heard on the grapevine)
I too am new to web design. I have two registered domains which I registered with Bluehost (recommended by WP and cheap) and installed WP on my CPanel.
WP was recommended to me by a local computer guy who has over 350 sites as being the easiest and most user friendly. He said Joomla to complicated if you're not a techie.
That's as far as I've got. Been overwhelmed with the plethora of themes out there, some fantastic looking ones, even the freebies. I've seen a couple that might fit with my eco sites but need tweaking and don't want to have to learn yet another language (code). Can anyone recommend a good outsourcer ?(not too expensive, have gone broke procrasting and run out of funds :-( )
I usually just use the default template then just edit it and created separate template files (using the code at the top with #templatename) then you can put whatever flash content etc you like in then and mix it amongst wordpress php code that will pick up the latest news or widgets etc.. so gives you complete freedom
Otherwise as for getting flash into posts hit the little 'embed media' button in the visual viewer and there is a flash option hope this helps.
I know yeah Greg's is good that's what first made me think Wordpress is a good platform. Especially for a newbie to web desin - like me... simple (well hopefully, once i get my head round it) to use, yet it can give a great result.
If you are completely new to web design / development, I would not recommend Wordpress; unless you are using the online version on Wordpress.com, as you will need existing knowledge to be able to install and edit Wordpress on your own server/host.