It is possible to integrate an AWeber signup form for your email marketing campaigns on a website that includes Flash content, but it may require some work with a designer.
The problem with Flash is that it doesn't provide a way to easily integrate form HTML, which is necessary for publishing one of our signup forms.
Still, essentially all webpages are composed in HTML, including Flash sites. In sites dominated by Flash content, there is generally a minimal amount of HTML, leaving what appears on the site to an embedded Flash object, but there is still HTML that the form can be added to.
What to Suggest to Your Designer
In order to integrate an AWeber form with your site, suggest to your designer that they add the form HTML before or after "the Flash object".
While this will instantly produce a page with a working sign up form on your site, they may need to adjust the overall design of the page so that the form appears in a place where subscribers will see it, without affecting the usability of the Flash portion of the site.