Henry V: Dye Room | Behind the Scenes | Stratford Shakespeare Festival
This 2012 video is from the Stratford Shakespeare Festival in Canada and shows a gambeson being over-dyed.
I love it when you can see the logo on the dyer's apron: Lee Valley Tools.
For a total co-incidence, a costume designer talks about over-dyeing military outfits from a different production of Henry V, in an article by Eliza Kessler, "Henry IV and Henry V: Q&A with the costume designer" BBC, July 5, 2012, http://www.bbc.co.uk/blogs/tv/2012/07/henry-iv-v-shakespeare.shtml. She also talks about research and practical considerations.