Trying to flesh out (haha, get it) my understanding of who was responsible for the dyeing of leather.
The period leather dye recipes are found in books with a mix of other skills. The manuals include fabric dyeing recipes but also recipes for how to tan leather, make parchment and a variety of other skills.
So, who did the actual dying? Was it done by the people who processed the skins (the tanner or currier), was there someone else in the process (dyers guild or a leather dyer) once the leather had been prepared, or was the leatherseller or end craftsman the one who dyed the skins?
Based on the way the recipes work, it seems like they would be used on whole skins, not just painted on smaller pieces of leather for a specific project. Given the nature of the recipes and how they are documented, I suspect it wouldn't be the seller or end craftsman, but rather would have been delivered already dyed for their use - really not that much different from how we get our leather today.
It probably varied by region but I'll start my research with London given their structured guild system and reasonably good records (despite the 1666 fire).
Some research links:
English industries of the Middle Ages, being an introduction to the Industrial history of mediaeval England
Contains a reference to "leather-dyers" as an industry as it indicates they were banned from dyeing certain types of low quality skins.
History and antiquities of the Worshipful company of leathersellers, of the city of London: with facsimiles of charters, and other illustrations
e-Book copy of a resource about the leathersellers company in London. Could have useful information about how the industry was structured. May reference dyeing of leather. Will need to look through it carefully.
The Art and Mysterie of the Currier
Information on the historical role of the currier/leather dresser, which mentions that once curried the leather could be dyed or stained. No mention of who did the dyeing.
Craft Guilds in the Early Modern Low Countries
A book on the structure and impact of craft guilds in Neatherlands as early as the 11th century. For when I expand my research beyond London.
Craft-guilds of the thirteeth century in Paris
A book from 1915 on the craft guilds in Paris in the 13th century. It mentions the tanners, the leather dressers and the curriers as three separate guilds in Paris as early as 1160.
York’s Guild’s Names in the 15th Century and their Translation into Spanish
Section 2.1 discusses the translation of the names of guilds that dealt with leather. This gives some ideas of the leather-related guilds that were operating in York. Also a list of names at the end of the document.