Change the front page based in the screen size of the visitor?
The responsiveness of Omega uses CSS3 Media Queries, which are totally client side.  The other thing to think about is that with true responsive design, the viewport of the client can change while viewing a single page, and the page should adapt.  For example, you can load a page in Chrome, and resize the browser window, and go through the narrow/normal/wide changes and see how responsive your site is.

My suggestion is to make your front page so you employ Progressive Enhancement and not Graceful Degredation.  Design the page so that it works well for users without Flash or Javascript, and make it responsive.  Then, when the page loads, have some JS that checks the browser width, and then use SWFObject to add in the Flash content using the dynamic method.  Depedning on your situation, you may want to add in some min-width and/or display: none on the Flash &lt;div&gt; in the narrow/normal/wide sheets to handle viewport changes.