Truth is no one knows. I suspect that Richards troops carried his banners. He fought in a seperate ward to the king and after all he was a Duke!
What is known is that Richard and Edward both kitted out there men with Livery and badges, Richard issued 5,000 boar badges at some time during the WotR and one of the things he did in his brief tenure as king was to create the College of Arms, before which there was no official control of Heraldry.