WebDriver is built on javascript. This is a standard which all browsers support. The implementation might be slightly different from browser to browser but the bulk of browsers tend to work the same.
Flash was created by MacroMedia and later acquired by Adobe. It is not open like javascript. It has security concerns which make some browsers block it. No published information on how it works, internally, makes it difficult to automate. When people figure out how to automate a version of Flash, there is no guarantee that the next version of Flash will work the same way. This often resulted in automation tools failing to work when new versions of Flash were released.
Add to the difficulty in creating automation tools for Flash, Adobe recently announced it was going to End Of Life (EOL) Flash. It recognized that HTML5 is supported on more platforms and people are switching to HTML5 for their application. Sites like YouTube switched to HTML5 a while ago.
So attempting to create automated tools and maintaining them for a technology which has known security concerns and no future doesn't make a lot of sense. Therefore, finding tools which will help with automating Flash is going to be problematic at best.
You are probably better off using a tool which automates desktop applications, rather than automating web applications, and automate the browser (with a Flash plugin) as a desktop application. Even though desktop automation really hasn't been a leading area of development since 1998, it is still more mature than Flash automation, especially on Windows platforms.
Darrell