No - webview will not support a flash player plugin. install flash plugin for WebView "Thread: install flash plugin for WebView"
Richard's comment from the thread (Richard is the JavaFX lead):
As for plugins, we are not likely to ever support running plugins (except maybe applets), for security reasons. There are also additional issues. If the browser is to support arbitrary things that Chrome supports like native client etc, it adds to the footprint of the browser (and security risks). Already the WebView constitutes over half of the download size of JavaFX. I would need a pretty strong justification to make it larger if doing so also increases our risk to vulnerabilities.