Is it a flash cookie or is it a program that is stored in a flash cookie?
Cookies are key/value pairs stored in the browser. ( https://en.wikipedia.org/wiki/HTTP_cookie
They are set by the server and JS running in the browser. Flash can access cookies via JS.
But a cookie can only hold a value, like number or text. It cannot "run a program".
Also, you can delete them as soon as you leave a page ( just use "incognito/privacy" mode )
Any page that you visit with your browser, probably uses JS to enable some functionality.
( you can turn JS off in your browser, so none of the JS code will be executed, but then most pages won't function properly )
Some pages ( like the bookmakers' ) might use JS to also pick on some data about your machine. But browsers, for security reasons, sandbox every page, so the data it can sniff on are limited.
There are many silly "what is your browser" pages ( like this https://www.whatismybrowser.com
) which seem to be knowing a lot about your machine.
But they infer most of the info.
For example, accessing a site via VPN, can mask your real public IP. So "location" will be not real.
Masking the user-agent can throw off anything that is inferred from that, etc.
So, it's complicated to know how each sites gathers data and what you need to change.
The more you can mask/change, the better. But it depends on what you are trying to hide.