Basically, just get the right Network Activity Indicator utility executable, for MS Windows, and run it under Wine. After searching extensively, I came to the conclusion that this utility has never been exactly duplicated on the GNU/Linux platform, so I gave this method a try.
I was surprised to see that it works, down to the last detail, even as to installing itself in the Panel, in the same location as in the MS Windows Desktop (previous versions, that is -- Microsoft removed it from recent versions).
Details in a "Newbie Questions' thread that dealt extensively with work-arounds and similar utilities, none of which exactly answered the OP's wish for a dual-screen animated network monitor.
My compliments to the Wine developers!