What is this message?

I'm thinking based on your frustration, that this dialog probably isn't responding to clicks.  There's a long explanation for why this happens, but long story short, we need to know for sure that you can see that dialog, and that it's unobscured.  We don't want a malicious actor to put something over a security dialog and then trick you into clicking it.

Unfortunately, if the dialog pops up over something with a lot of motion around it (like a game or video), it's not always possible to know for sure that you can see the dialog, and we err or the side of caution and assume that something isn't right.

This dialog doesn't show by default.  You have to change Flash Player's default storage settings in order for it to pop up.  The benefits you bet by doing that (privacy) are largely superstition in 2017, as the ability for marketers to track you has largely been supplanted by more powerful HTML5 capabilities, and network/server side tracking techniques facilitated by large ad networks and more recently, Internet Service Providers. 

You're better off leaving the settings at default, and using a paid VPN service, in tandem with your browser's private browsing/incognito mode, if you really want to avoid being tracked.  We respect private browsing mode, and data from both Flash and HTML/JavaScript that accumulated during your private browsing session is deleted when you exit.  This addresses most of the resilient techniques for modern behavior tracking.  Also, in browsers that send us a notification (which is most modern browsers), when you clear your browser cookies, we also blow away Flash Player's local stored objects (a.k.a LSOs, or "Flash Cookies" in the colloquial).

Anyway, if you're using anything but Google Chrome, you can go to Settings / Control Panel > Flash Player > Storage and choose Allow Sites to Store Information on This Computer, and we'll suppress that dialog. 

If you're on Chrome, go here: Adobe - Flash Player : Settings Manager - Global Storage Settings Panel

Set the slider to Unlimited, and check Never Ask Again.

Hi,

This the Local storage permission dialogue. When the Flash game you are trying to play wants to store some related data on to your Flash's local storage path, it pops-up this dialogue. You may choose to allow or deny the local storage access on your system. Once you choose your option the dialogue will disappear.

Thanks!