The below information was taken from a quick search on this subject.
Simple answer - No!
The browser has no way to know what's going on inside a flash object.
There are ways to tell if Flash object control has finished loading via Javascript.
This Adobe page talks about some methods accesible from javascript including the OnReadyStateChange(state) which is generated when the ready state of the control changes. The possible states are: 0=Loading, 1=Uninitialized, 2=Loaded, 3=Interactive, 4=Complete. The argument type is integer.
However - VBA code does not equal javascript (and the two are not generally on speaking terms)
Plus one flash move can be chained onto loading another.
So even if you could tap into the Flash methods via javascript you only know when the first .swf file was loaded, not any subsequent ones.
Plus Adobe is happily engaged in trying to break any sort of compatibility between its Flash product and VB.
Here's a little discussion thread that talks about the VB breakage that happened after Flash version 10e:
http://forums.adobe.com/thread/662931
I should also add that if it probably can't be done in IE it definitely can't be done in a browser like Firefox.
Someone named Adam Lock had the courage/stupidity to try an create a Firefox ocx.
The page still exists even though the project has been abandoned since an early 1.x version of Firefox:
http://www.iol.ie/~locka/mozilla/control.htm#usingVB
Basically trying to use COM with Firefox was just too much of a stretch and the Firefox community as a whole doesn't seem to want Firefox to be ActiveX friendly at all.
Flash can work with VB/VBA but really only if you have the source code (.fla) for the Flash .swf in question (and specifically write actionscript code sending out the data/info into the browser via using FSCommand).
This link would be a good starting point for that sort of thing, but since it appears someone else at your company is control of the Flash development you are probably just outta luck.
So unless things have changed, Im guessing the time and energy that you would invest in this function would be outweighed by actually entering the data.<!-- / message -->