Rapp's memoirs talk about presenting some banners and that Gerard's painting was loosely based on the event. Here is nice explanation of the painting -
https://en.wikipedia.org/wiki/Battle_of_Austerlitz,_2_December_1805_(G%C3%A9rard) I think it is essentially propaganda very, loosely based on a number of facts - capturing a banner was a nice way to secure promotion and usually a reward among other things.
I have not seen anything that actually mentions such an event. Still it does make for some stirring flats, the flags of which are very well documented so why not.
mark
P.S. The Segom set showing the presentation of flags after Ligny/Quatre Bas is another event that never happened but, it is a clever presentation and looks like a very nice set.