May be a dumb question, but GWT FlowPanel (raw div element) does not provides something to handle a mouseclick/mousemovement on it. Overriding onBrowserEvent do not works either.
If setting onclick event using native JavaScript (need to specify positive height before, 'div' have a height of 0 if not specified), then catching these events is working properly. Is there a way to do it without using JSNI?
Seems question is a dumb one, yes. FlowPanel can be easily wrapped or replaced with FocusPanel, which provides a lot of method for monitoring/handling events.
What you need to do here is wrap your FlowPanel in a FocusPanel. A FocusPanel contain all possible handler and thus will enable you to have a ClickHandler set to it.
Another method would be to create your own widget extending the flowpanel and implementing the necessary interface in order to be able to contain a ClickHandler.
I personally would recommend the first method. It's simpler, faster to code and won't slow down your application.