You could just download a distribution such as Fedora (I would pick Fedora if you are new to Linux) and then install it and once that's done go to http://www.macromedia.com and hit the download button on the download flash page. It will detect you are on Linux and give you the proper file.
Ah! I understand the confusion now... I wasn't talking about the Flash plugin, I was talking about the full, out-of-the-box Flash MX 2004 version that now costs about $500 ($200 for an upgrade). The actual Flash studio with which one makes Flash files.