Flash looks great and can make your site look very professional. But it is not SEO-friendly unless the web designer knows how to do it.
Would it frustrate me? Yes, if I am looking for a direct answer to a question, and I need it NOW, I don't have time to wait for a Flash video to download. Besides, I"m visually impaired. If the Flash website has very small text and fancy design, it makes it harder for me to read and navigate. Oh, and if the site tells me, "You need to upgrade to the latest version of Flash" or something, I'll go elsewhere. Why bother? There are countless other options.
BUT there are people who love Flash sites. If it didn't work, why do you think there are Flash themes going for thousands of dollars (exclusive rights)? I personally know somebody who wants to purchase a Flash design for their business site and I think it's a smart move. But then their audience is very specific and established. So they follow that person no matter what.
What I'd suggest is, why don't you make a plain HTML/CSS site and a Flash version? It would give users the option. The only problem is you'd have two sites to upgrade. Or, if you do use Flash, make sure the web designer is also a proven SEO expert. I'm no a programmer (been YEARS since I messed with websites) but I know if the coding isn't right, Flash will hurt your search engine ranking.
Also consider the nature of your business. Why and how do people find your site? Are they looking for specific info like "How do you start a baby on solid foods?" or "Best chicken soup recipe ever"? If your site is mainly information oriented, you probably won't need Flash; you'd need lots of informative articles. But if the site has to be aesthetically pleasing, then maybe upgrading to Flash would be appropriate.
Good luck!