Adobe Flash cookies work through the ubiquitous Adobe Flash and enables any of Adobe's partners to set global cookies that are maintained on Adobe's servers instead of your own computer. Adobe Flash cookie partners include sites such as Microsoft, Disney, Weather.com, Paypal, eWeek, Flickr and many others. This means that no matter how, or how often, you try to delete your cookies, just having Adobe Flash installed negates that effort.
To delete or deny these offsite cloud cookies, you will need to visit the Adobe Flash Player Settings Manager webpage, click the Website Privacy Settings Panel, delete the 'Visited Websites' list and then select 'Always Deny' (or 'Always Ask' to choose on a case-by-case basis).
It's worth noting that having Adobe Flash installed also enables websites to access your webcam and microphone settings. While you're at the Adobe Flash Player Settings Manager, you may want to block this unauthorized access as well.