It depends rather on what you mean by Flash website. Every Flash site has an underlying HTML page, and you can include the Twitter widget there, possibly from outside the Flash editing environment. You may also be able to overlay the widget frame over the Flash content in an appropriate place, using CSS positioning to place it fixed in the browser, and leaving a space of the same size in the Flash layout.
Within the Flash content itself, the Timeline widget is purely for HTML and CSS deployment; we do not have plans to build a Flash-native widget.
For that use, there may be existing Tweet rendering tools out there that other developers have written, but fundamentally you’ll need to use the API to fetch Tweets and render them manually within the Flash content.