Pay very close attention to the product needed. There are Flash PLAYER, free software for viewing animations and movies in web sites, and Flash (without PLAYER in the name), used to author/create/edit animations for web sites.
If Flash Player, get the current product. It is free.Do not use old software, it has serious security issues. http://get.adobe.com/flash .
If Flash, specifically Macromedia Flash 8, this was a product released in 2005, and replaced in 2007 by Adobe Flash CS3 Professional. A license was needed, and has not been sold for many years. If the license is lost, there is no chance to run the software, which in any case isn't for modern systems. The current successor to Flash 8 is version 19 and is called Adobe Animate CC 2019. This is available only on subscription, and is available separately or part of the all apps Creative Cloud.
You might also mention to your user, if it is in your brief, that Flash Player is being phased out and will be gone by the year 2020. If this is part of your web site strategy, now is the time to review all options.