Well, let's take a look and decompose the costume, shall we?
The coat's base is definitely a heavy cloth, something that drapes well. In a perfect world, I'd go with a wool or wool blend. Failing that a velvet (but not a fake/panne/crush velvet - eww).
The shoulders and upper-arm strappings is clearly leather. Though something of medium thickness - you don't want it too thick as to be unworkable, but too thin as to be too flimsy. Same material as the boots. The wings should be bound in leather, not made entirely from it, or you won't get the support you're looking for.
The inner shirt and coat lining (I would be tempted to make this as two pieces, but that may not be functional) should be linen rather than cotton.
The glove is strapping. Strips of red linen would be perfect - get someone who knows how to wrap a bandage to help you out. Consider it a conspiracy theory, but I suspect that "glove" is designed to stabilise the hand and help avoid RSI (repetitive strain injury) associated with holding those heavy books.
If my hunch is correct, the intent of the gilding on the cuffs and hems is to articulate and flow of aether around the summoner, much like the ornamentation on the Veil of Wiyu. A fabric using metallic thread would be optimal, but a shiny brocade would probably work as well.