Flash does not usually remove its cookies when you delete your browser history. It keeps its data in a place separate from regular web pages, and it will persist after you clear your cache.
According to this Reddit post by setting cookies through Flash, Web sites can store data on your computer that is not removed when you clear your cache.
How can you access this information? Visit the Abobe Settings Manager page to see a list of all the sites that are using Flash to store data on your computer, much of which is probably for identifying purposes. Through this settings manager, you can delete these cookies.
There is also an open Chromium report on the topic, in which one commenter notes that this is a common data store shared between all the Flash-enabled browsers on your computer.