I wouldn't do the auto-remove from Fantastico, as it may delete parts of your site.

As why your new site comes up when you click to access joomla it's either;
1. You overwrote index.php
2. Your new site is index.html[or .htm], which will show before index.php.

To remove joomla, I would go in manually and delete each file one at a time, to make sure you don't mess anything up. Or, you can make a full backup of your site, and try the auto-remove in Fantastico. Before doing the auto-remove, make sure to download a backup of your site.

Please make sure that you have no redirects to that directory as any redirects will cause the website to resolve to the joomla content you had previously. As also suggested you can remove it as well if you already have the flash content live for the domain and you are wanting visitors to directed to the newly flash content.

If you did previously have joomla removed and there was any restoration done to your account it is a slim chance that it may have been restored along with any new content. I can only provide suggestions as your information is still a little vague to the issue you are having. To rather you wish to keep the joomla content or you have issues with traffic being sent to the old content.