I'm pretty good at designing flash animations and such. I don't think the term you mean is exactly "flash intro". As long you don't have a flash animation as your homepage, with a second page as your actual home page, then you probably won't make anyone cringe.
I think I know what you're talking about... like a banner on the top of the page, maybe about 300-500 pixels tall, maybe about the full width of the screen, usually shows project highlights, or pictures. Maybe product features or a quick way to explain your company visually without so much copy?
If you could link to an example, or screenshot that would be most helpful.
Let me know if I can help you on this.
- Josh