Yes they did use banners but they were not of official design and often had a religious theme.
See Stephen Summerfield (2004) Cossack Hurrah, Russian cosscks and irregular cavalry of the Napoleonic Wars, Partizan Press has at least two colour plates on them.
There is nothing in both Ospreys upon the cossacks. There are the Vistigov plates that a kind sole may give you a URL. Mark Conrads site would also be useful to consult but details are scarce.