For years Flash has been one of the limiters that prevented many people from completely switching to Linux. Fully featured development tools weren't available and many distros don't even ship with the ability to view Flash due to it being non-free. And even when a Flash plug-in was added by the user there were still some sites that would not load because they required version 8 or higher. Adobe recently announced the Flash 9 for Linux beta to address the latter issue, but you might be surprised to know that a common application that may already be installed is capable of creating Flash presentations. I'm talking about OpenOffice.org Impress.
Using Impress is by no means a perfect situation, but it can be very useful for simple projects. The first step is creating the presentation just like you would any other. Once you have the content completed, go to the File menu and choose Export. Change the File Format to Macromedia Flash (SWF), enter a file name, and click Export. That's it. Now you can freely distribute you shiny new .swf file and it will be viewable in any Flash enabled browser.
If your Flash needs are more sophisticated there are other options. KToon, Uira, F4L, and OpenLaszlo all bring additional capabilities to the table. KToon and Uira are designed for vector animation. F4L (Flash for Linux) aims to become a complete Flash creation environment. And OpenLaszlo is designed for generating rich web content.